diff --git a/01_nb_cncf_optimization/.ipynb_checkpoints/gen_nb_cost_optimization-checkpoint.ipynb b/01_nb_cncf_optimization/.ipynb_checkpoints/gen_nb_cost_optimization-checkpoint.ipynb
deleted file mode 100644
index 4675328..0000000
--- a/01_nb_cncf_optimization/.ipynb_checkpoints/gen_nb_cost_optimization-checkpoint.ipynb
+++ /dev/null
@@ -1,473 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "ab5cd7d1-1a57-46fc-8282-dae0a6cc2944",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "import numpy as np\n",
-    "import random"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "id": "3d1ad0b9-f6a8-4e98-84aa-6e02e4279954",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "DATABASE_OBJECT_COUNT = 100\n",
-    "CACHE_SIZE = DATABASE_OBJECT_COUNT/2\n",
-    "ZIPF_CONSTANT = 2\n",
-    "\n",
-    "CACHE_MISS_COST = 2\n",
-    "CACHE_REFRESH_COST = 1\n",
-    "\n",
-    "SEED = 42\n",
-    "np.random.seed(SEED)\n",
-    "random.seed(SEED)\n",
-    "\n",
-    "LAMBDA_VALUES = np.array([np.random.zipf(ZIPF_CONSTANT) for i in np.arange(1, DATABASE_OBJECT_COUNT + 1,1)])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "id": "9cc83cf6-5c78-4f0d-b7cb-08cdb80c362e",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# LAMBDA_VALUES = np.array([0.03, 0.04,0.05,0.06,0.07,1,1.1,1.2,1.3,1.4,1.5])\n",
-    "# DATABASE_OBJECT_COUNT = len(LAMBDA_VALUES)\n",
-    "# CACHE_SIZE = 4.4\n",
-    "# CACHE_MISS_COST = 7\n",
-    "# CACHE_REFRESH_COST = 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "id": "3dc07233-0b56-4fee-a93b-212836c18b42",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "db_object_count = DATABASE_OBJECT_COUNT\n",
-    "cache_sz = CACHE_SIZE\n",
-    "\n",
-    "lambda_vals = LAMBDA_VALUES\n",
-    "c_f = CACHE_MISS_COST\n",
-    "c_delta = CACHE_REFRESH_COST"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "5a27d416-8f98-4814-af9e-6c6bef95f4ef",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals):\n",
-    "    num = (db_object_count * c_f - cache_sz * c_delta)\n",
-    "    denom = np.sum(1.0/lambda_vals)\n",
-    "    return max(0, num/denom)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "id": "6276a9ce-f839-4fe6-90f2-2195cf065fc8",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def h_i_star(c_f, eta, lambda_vals, c_delta):\n",
-    "    optimized_hitrate = (c_f - (eta/lambda_vals)) / c_delta\n",
-    "    return optimized_hitrate"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "id": "dcd31a8c-6864-4b9a-8bb3-998f0c32baf6",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n",
-    "    local_hitrates = hitrates[(hitrates < 0) | (hitrates > 1)]\n",
-    "    smallest_delta = np.abs(np.min(local_hitrates))\n",
-    "    biggest_delta = np.max(local_hitrates) - 1\n",
-    "    if smallest_delta > biggest_delta:\n",
-    "        index = np.where(hitrates == np.min(local_hitrates))[0][0]\n",
-    "        return index\n",
-    "    else:\n",
-    "        index = np.where(hitrates == np.max(local_hitrates))[0][0]\n",
-    "        return index"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "id": "55b251f8-97ca-49a8-9ec6-be77dc1e49b2",
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [],
-   "source": [
-    "\"\"\"\n",
-    "Perform theoretical optimization to compute optimal hit probabilities.\n",
-    "\n",
-    "Parameters:\n",
-    "- lambda_vals (numpy array): Request rates for each item.\n",
-    "- B (float): Total cache size.\n",
-    "- c_f (float): Fetching linear cost (cache miss cost).\n",
-    "- c_delta (float): Age linear cost.\n",
-    "\n",
-    "Returns:\n",
-    "- h_opt (numpy array): Optimal hit probabilities for each item.\n",
-    "\"\"\"\n",
-    "optimized_hitrates = np.zeros(DATABASE_OBJECT_COUNT)\n",
-    "differenc_set = np.arange(DATABASE_OBJECT_COUNT)\n",
-    "fix_i = []\n",
-    "current_db_objects = DATABASE_OBJECT_COUNT\n",
-    "current_cache_size = CACHE_SIZE\n",
-    "\n",
-    "while True:\n",
-    "    if current_db_objects == 0:\n",
-    "        # Handle special case: no items left to optimize\n",
-    "        if current_cache_size > 0:\n",
-    "            # Redistribute unused cache size among items with zero hit probability\n",
-    "            differenc_set = np.where(optimized_hitrates == 0)[0]\n",
-    "            fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set)\n",
-    "            current_db_objects = len(differenc_set)\n",
-    "            continue\n",
-    "        else:\n",
-    "            optimized_hitrates[differenc_set] = 0\n",
-    "            break\n",
-    "    # Compute Lagrangian multiplier and optimal hit probabilities\n",
-    "    mu = max(0, (current_db_objects * c_f - current_cache_size * c_delta) / np.sum(1.0 / lambda_vals[differenc_set]))\n",
-    "    eta = eta_star(current_db_objects, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n",
-    "    assert(mu == eta)\n",
-    "    optimized_hitrates[differenc_set] = (c_f - mu / lambda_vals[differenc_set]) / c_delta\n",
-    "    # print(optimized_hitrates)\n",
-    "    # Handle the case where mu < 0\n",
-    "    if mu < 0:\n",
-    "        current_cache_size = current_db_objects * c_f / c_delta  # Adjust cache size for next iteration\n",
-    "        continue\n",
-    "    # Check for constraint violations\n",
-    "    larger_i = np.where(optimized_hitrates > 1)[0]  # h > 1\n",
-    "    smaller_i = np.where(optimized_hitrates < 0)[0]  # h < 0\n",
-    "    # If no violations, optimization is complete\n",
-    "    break_con = len(smaller_i) == 0 and len(larger_i) == 0\n",
-    "    break_con1 = len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0\n",
-    "    assert(break_con == break_con1)\n",
-    "    if break_con:\n",
-    "        break\n",
-    "    # Find the furthest violating item\n",
-    "    min_viol, min_viol_i = (0, -1)\n",
-    "    if len(smaller_i) > 0:\n",
-    "        min_viol_i = np.argmin(optimized_hitrates)\n",
-    "        min_viol = optimized_hitrates[min_viol_i]\n",
-    "    max_viol, max_viol_i = (0, -1)\n",
-    "    if len(larger_i) > 0:\n",
-    "        larger = optimized_hitrates - 1\n",
-    "        max_viol_i = np.argmax(larger)\n",
-    "        max_viol = larger[max_viol_i]\n",
-    "    # Compare the furthest violations and adjust accordingly\n",
-    "    viol_i = min_viol_i\n",
-    "    min_viol_flag = True  # True if furthest is from the left boundary\n",
-    "    if max_viol > abs(min_viol):\n",
-    "        viol_i = max_viol_i\n",
-    "        min_viol_flag = False    \n",
-    "    index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
-    "    if viol_i != index:\n",
-    "        print(optimized_hitrates[viol_i])\n",
-    "        print(optimized_hitrates[index])\n",
-    "        assert(viol_i == index)\n",
-    "    if min_viol_flag:\n",
-    "        optimized_hitrates[viol_i] = 0\n",
-    "    else:\n",
-    "        optimized_hitrates[viol_i] = min(1, current_cache_size)\n",
-    "\n",
-    "    # Update parameters for next iteration\n",
-    "    current_cache_size =- optimized_hitrates[viol_i]\n",
-    "    fix_i.append(viol_i)\n",
-    "    differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
-    "    current_db_objects = DATABASE_OBJECT_COUNT - len(fix_i)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "id": "efa16eaf-a10b-4927-99cd-190e2ffe1d1e",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "a = optimized_hitrates\n",
-    "b = differenc_set"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c",
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "All values optimized.\n"
-     ]
-    }
-   ],
-   "source": [
-    "\"\"\"\n",
-    "Perform theoretical optimization to compute optimal hit probabilities.\n",
-    "\n",
-    "Parameters:\n",
-    "- lambda_vals (numpy array): Request rates for each item.\n",
-    "- B (float): Total cache size.\n",
-    "- c_f (float): Fetching linear cost (cache miss cost).\n",
-    "- c_delta (float): Age linear cost.\n",
-    "\n",
-    "Returns:\n",
-    "- h_opt (numpy array): Optimal hit probabilities for each item.\n",
-    "\"\"\"\n",
-    "optimized_hitrates = np.zeros(DATABASE_OBJECT_COUNT)\n",
-    "differenc_set = np.arange(DATABASE_OBJECT_COUNT)\n",
-    "fix_i = []\n",
-    "current_db_objects = DATABASE_OBJECT_COUNT\n",
-    "current_cache_size = CACHE_SIZE\n",
-    "\n",
-    "while True:\n",
-    "    if current_db_objects == 0:\n",
-    "        # Handle special case: no items left to optimize\n",
-    "        if current_cache_size > 0:\n",
-    "            # Redistribute unused cache size among items with zero hit probability\n",
-    "            differenc_set = np.where(optimized_hitrates == 0)[0]\n",
-    "            fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set)\n",
-    "            current_db_objects = len(differenc_set)\n",
-    "            continue\n",
-    "        else:\n",
-    "            optimized_hitrates[differenc_set] = 0\n",
-    "            break\n",
-    "    # Compute Lagrangian multiplier and optimal hit probabilities\n",
-    "    eta = eta_star(current_db_objects, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n",
-    "    optimized_hitrates[differenc_set] = (c_f - eta / lambda_vals[differenc_set]) / c_delta\n",
-    "\n",
-    "    if mu < 0:\n",
-    "        current_cache_size = current_db_objects * c_f / c_delta  # Adjust cache size for next iteration\n",
-    "        continue\n",
-    "    \n",
-    "    if len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0:\n",
-    "        print(\"All values optimized.\")\n",
-    "        break\n",
-    "    max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
-    "    optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n",
-    "\n",
-    "    current_cache_size =- optimized_hitrates[max_outbound_index]\n",
-    "    fix_i.append(max_outbound_index)\n",
-    "    differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
-    "    current_db_objects = DATABASE_OBJECT_COUNT - len(fix_i)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "id": "4f64253f-b389-4be9-b403-08027d480121",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
-       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
-       "       0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.,\n",
-       "       1., 0., 0., 0., 0., 0., 1., 0., 0., 1., 0., 0., 0., 0., 1., 0., 1.,\n",
-       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.,\n",
-       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.])"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "optimized_hitrates"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "id": "17d818db-ec88-4c26-92af-6d74862525d9",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.43902439,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.43902439,  0.        ,  0.        ,\n",
-       "        0.        ,  0.04878049,  0.        ,  0.04878049,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        , -0.        ,  0.        ,\n",
-       "        0.04878049,  0.04878049,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.43902439,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "       -0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "       -0.        ,  0.        ,  1.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        , -0.        ,  0.        ,\n",
-       "        0.        ,  0.43902439,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.04878049,  0.        ])"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "a"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "id": "791b3f96-527a-489e-970e-c92ec950177f",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6, 27, 31, 33, 40, 41, 50, 81, 98])"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "b"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "id": "c22fa973-432a-4c05-89bf-2a6ea82ae3d2",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6, 27, 50, 81])"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "differenc_set"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "id": "898e1266-5aaa-46f4-ac0f-c7807ac2b6bb",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "db_object_count = DATABASE_OBJECT_COUNT\n",
-    "cache_sz = CACHE_SIZE\n",
-    "loop_lambda = lambda_vals\n",
-    "\n",
-    "non_optimized_values = np.arange(db_object_count)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "id": "8cc9b8a9-f7ae-48fc-adfb-ac4b7a4998f1",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "db_object_count = DATABASE_OBJECT_COUNT\n",
-    "cache_sz = CACHE_SIZE\n",
-    "loop_lambda = lambda_vals\n",
-    "\n",
-    "optimized_hitrate = np.zeros(db_object_count)\n",
-    "non_optimized_values = np.arange(db_object_count)\n",
-    "optimized_value = {}\n",
-    "\n",
-    "eta = eta_star(db_object_count, c_f, cache_sz, c_delta, loop_lambda[non_optimized_values])\n",
-    "optimized_hitrate[non_optimized_values] = h_i_star(c_f, eta, loop_lambda[non_optimized_values], c_delta)\n",
-    "\n",
-    "max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrate)\n",
-    "optimized_value[max_outbound_index] = (1 if optimized_hitrate[max_outbound_index] > 1 else 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "id": "cbcf3592-fcf2-4f54-a3cd-761097c12972",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{67: 1}"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "optimized_value"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "db732331-1d09-45b7-915c-73daa270b5e2",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "graphs",
-   "language": "python",
-   "name": "graphs"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.7"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/01_nb_cncf_optimization/.ipynb_checkpoints/nb_cost_optimization-checkpoint.ipynb b/01_nb_cncf_optimization/.ipynb_checkpoints/nb_cost_optimization-checkpoint.ipynb
index 725cd1d..88de62d 100644
--- a/01_nb_cncf_optimization/.ipynb_checkpoints/nb_cost_optimization-checkpoint.ipynb
+++ b/01_nb_cncf_optimization/.ipynb_checkpoints/nb_cost_optimization-checkpoint.ipynb
@@ -9,7 +9,8 @@
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
-    "import random"
+    "import random\n",
+    "import pandas as pd"
    ]
   },
   {
@@ -23,7 +24,7 @@
     "CACHE_SIZE = DATABASE_OBJECT_COUNT/2\n",
     "ZIPF_CONSTANT = 2\n",
     "\n",
-    "CACHE_MISS_COST = 1\n",
+    "CACHE_MISS_COST = 2\n",
     "CACHE_REFRESH_COST = 1\n",
     "\n",
     "SEED = 42\n",
@@ -95,62 +96,201 @@
    "outputs": [],
    "source": [
     "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n",
-    "    local_hitrates = hitrates[(hitrates < 0) | (hitrates > 1)]\n",
-    "    smallest_delta = np.abs(np.min(local_hitrates))\n",
-    "    biggest_delta = np.max(local_hitrates) - 1\n",
+    "    lower_bound_violation =  hitrates[(hitrates < 0)]\n",
+    "    upper_bound_violation = hitrates[(hitrates > 1)]\n",
+    "    smallest_delta = np.abs(np.min(lower_bound_violation))\n",
+    "    biggest_delta = np.max(upper_bound_violation) - 1\n",
     "    if smallest_delta > biggest_delta:\n",
+    "        print(smallest_delta)\n",
     "        index = np.where(hitrates == np.min(local_hitrates))[0][0]\n",
     "        return index\n",
     "    else:\n",
+    "        \n",
     "        index = np.where(hitrates == np.max(local_hitrates))[0][0]\n",
     "        return index"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
-   "id": "ccd4b95d-1cdd-4c99-a22e-4b31338993cf",
+   "execution_count": 8,
+   "id": "9d774304-ae68-43b3-a76a-e970c06c5236",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n",
+    "    outside_bounds = (hitrates < 0) | (hitrates > 1)\n",
+    "    distances = np.where(outside_bounds, np.maximum(np.abs(hitrates - 0), np.abs(hitrates - 1)), -np.inf)\n",
+    "    index = np.argmax(distances)\n",
+    "    return index"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "19678083-15e1-439b-be8c-42033d501644",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
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-       "       0.30256805, 0.86051361, 0.30256805, 0.30256805, 0.30256805,\n",
-       "       0.65128403, 0.30256805, 0.30256805, 0.30256805, 0.65128403,\n",
-       "       0.65128403, 0.30256805, 0.30256805, 0.76752268, 0.30256805,\n",
-       "       0.30256805, 0.30256805, 0.30256805, 0.65128403, 0.30256805,\n",
-       "       0.30256805, 0.30256805, 0.86051361, 0.30256805, 0.30256805,\n",
-       "       0.30256805, 0.82564201, 0.30256805, 0.82564201, 0.30256805,\n",
-       "       0.30256805, 0.30256805, 0.76752268, 0.91282101, 0.30256805,\n",
-       "       0.82564201, 0.82564201, 0.65128403, 0.30256805, 0.30256805,\n",
-       "       0.30256805, 0.93025681, 0.30256805, 0.30256805, 0.30256805,\n",
-       "       0.86051361, 0.92250756, 0.30256805, 0.30256805, 0.30256805,\n",
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-       "       0.65128403, 0.30256805, 0.30256805, 0.30256805, 0.76752268,\n",
-       "       0.65128403, 0.65128403, 0.76752268, 0.95350454, 0.30256805,\n",
-       "       0.30256805, 0.86051361, 0.65128403, 0.30256805, 0.30256805,\n",
-       "       0.65128403, 0.30256805, 0.65128403, 0.30256805, 0.30256805,\n",
-       "       0.65128403, 0.65128403, 0.76752268, 0.30256805, 0.65128403,\n",
-       "       0.30256805, 0.30256805, 0.98115049, 0.82564201, 0.65128403])"
+       "array([ 1,  3,  1,  1,  2,  1,  5,  1,  1,  1,  2,  1,  1,  1,  2,  2,  1,\n",
+       "        1,  3,  1,  1,  1,  1,  2,  1,  1,  1,  5,  1,  1,  1,  4,  1,  4,\n",
+       "        1,  1,  1,  3,  8,  1,  4,  4,  2,  1,  1,  1, 10,  1,  1,  1,  5,\n",
+       "        9,  1,  1,  1,  1,  1, 17,  2,  1, 26,  1,  1,  2,  1, 10,  1, 69,\n",
+       "        1,  1,  2,  1,  1,  1,  3,  2,  2,  3, 15,  1,  1,  5,  2,  1,  1,\n",
+       "        2,  1,  2,  1,  1,  2,  2,  3,  1,  2,  1,  1, 37,  4,  2])"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "eta = eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals)\n",
-    "optimized_hitrates = (c_f - eta / lambda_vals) / c_delta\n",
+    "lambda_vals"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "ccd4b95d-1cdd-4c99-a22e-4b31338993cf",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2.1159070575516945\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([-0.11590706,  1.29469765, -0.11590706, -0.11590706,  0.94204647,\n",
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+       "       -0.11590706,  1.47102324, -0.11590706, -0.11590706, -0.11590706,\n",
+       "        1.29469765,  1.73551162, -0.11590706,  1.47102324,  1.47102324,\n",
+       "        0.94204647, -0.11590706, -0.11590706, -0.11590706,  1.78840929,\n",
+       "       -0.11590706, -0.11590706, -0.11590706,  1.76489922, -0.11590706,\n",
+       "       -0.11590706, -0.11590706, -0.11590706, -0.11590706,  1.87553488,\n",
+       "        0.94204647, -0.11590706,  1.91861896, -0.11590706, -0.11590706,\n",
+       "        0.94204647, -0.11590706,  1.78840929, -0.11590706,  1.96933468,\n",
+       "       -0.11590706, -0.11590706,  0.94204647, -0.11590706, -0.11590706,\n",
+       "       -0.11590706,  1.29469765,  0.94204647,  0.94204647,  1.29469765,\n",
+       "        1.85893953, -0.11590706, -0.11590706,  0.94204647, -0.11590706,\n",
+       "       -0.11590706,  0.94204647, -0.11590706,  0.94204647, -0.11590706,\n",
+       "       -0.11590706,  0.94204647,  0.94204647,  1.29469765, -0.11590706,\n",
+       "        0.94204647, -0.11590706, -0.11590706,  1.94281332,  1.47102324,\n",
+       "        0.94204647])"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "eta = eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals[lambda_vals != lambda_vals[6]])\n",
+    "print(eta)\n",
+    "optimized_hitrates = (c_f - eta / lambda_vals[lambda_vals != lambda_vals[6]]) / c_delta\n",
     "optimized_hitrates"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 11,
+   "id": "05b17074-719f-4bca-8434-2aaee26094d0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>0</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>count</th>\n",
+       "      <td>96.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>mean</th>\n",
+       "      <td>0.437500</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>std</th>\n",
+       "      <td>0.726101</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>min</th>\n",
+       "      <td>-0.115907</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>25%</th>\n",
+       "      <td>-0.115907</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>50%</th>\n",
+       "      <td>-0.115907</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>75%</th>\n",
+       "      <td>0.942046</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>max</th>\n",
+       "      <td>1.969335</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "               0\n",
+       "count  96.000000\n",
+       "mean    0.437500\n",
+       "std     0.726101\n",
+       "min    -0.115907\n",
+       "25%    -0.115907\n",
+       "50%    -0.115907\n",
+       "75%     0.942046\n",
+       "max     1.969335"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pd.DataFrame(optimized_hitrates).describe()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
    "id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c",
    "metadata": {
     "scrolled": true
@@ -160,6 +300,48 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "Optimized: 67 1.97 // [ 1.79077042 -0.09229584  1.         -0.09229584 -0.09229584]\n",
+      "Optimized: 97 1.94 // [-0.07876743 -0.07876743  1.          1.48030814  0.96061628]\n",
+      "Optimized: 60 1.92 // [ 0.96720258 -0.06559484  1.         -0.06559484 -0.06559484]\n",
+      "Optimized: 57 1.88 // [-0.05274002 -0.05274002  1.          0.97362999 -0.05274002]\n",
+      "Optimized: 78 1.86 // [ 0.97977406  1.31984937  1.         -0.04045188 -0.04045188]\n",
+      "Optimized: 46 1.80 // [-0.02836604 -0.02836604  1.         -0.02836604 -0.02836604]\n",
+      "Optimized: 65 1.80 // [ 0.99140044 -0.01719911  1.         -0.01719911  1.        ]\n",
+      "Optimized: 51 1.78 // [-0.00600086  1.59879983  1.         -0.00600086 -0.00600086]\n",
+      "Optimized: 38 1.75 // [0.00491746 1.33497249 1.         0.00491746 1.50122936]\n",
+      "Optimized: 6 1.60 // [1.00774103 0.01548205 1.         0.01548205 0.01548205]\n",
+      "Optimized: 27 1.60 // [0.02399435 0.02399435 1.         0.02399435 0.02399435]\n",
+      "Optimized: 50 1.61 // [0.03255485 0.03255485 1.         1.         0.03255485]\n",
+      "Optimized: 81 1.61 // [0.04116395 0.04116395 1.         1.02058197 0.04116395]\n",
+      "Optimized: 31 1.51 // [0.04982206 0.04982206 1.         0.04982206 1.51245552]\n",
+      "Optimized: 33 1.51 // [1.         0.05714286 1.         0.05714286 0.05714286]\n",
+      "Optimized: 40 1.52 // [1.         0.06451613 1.         1.51612903 1.03225806]\n",
+      "Optimized: 41 1.52 // [0.07194245 1.         1.         1.03597122 0.07194245]\n",
+      "Optimized: 98 1.52 // [0.07942238 1.         1.         1.03971119]\n",
+      "Optimized: 1 1.36 // []\n",
+      "Optimized: 18 1.36 // [0.09223301 0.09223301 1.         0.09223301 0.09223301]\n",
+      "Optimized: 37 1.37 // [0.09756098 0.09756098 1.         1.         0.09756098]\n",
+      "Optimized: 74 1.37 // [0.10294118 0.10294118 1.         1.05147059 1.05147059]\n",
+      "Optimized: 77 1.37 // [1.05418719 1.05418719 1.         1.         0.10837438]\n",
+      "Optimized: 92 1.37 // [1.05693069 1.05693069 1.         0.11386139 1.05693069]\n",
+      "Optimized: 4 1.06 // [0.11940299 0.11940299 1.         0.11940299 1.        ]\n",
+      "Optimized: 10 1.06 // [0.12030075 0.12030075 1.         0.12030075 0.12030075]\n",
+      "Optimized: 14 1.06 // [0.12121212 0.12121212 1.         1.06060606 0.12121212]\n",
+      "Optimized: 15 1.06 // [0.1221374 1.        1.        0.1221374 0.1221374]\n",
+      "Optimized: 23 1.06 // [0.12307692 0.12307692 1.         0.12307692 0.12307692]\n",
+      "Optimized: 42 1.06 // [1.         1.         1.         0.12403101 0.12403101]\n",
+      "Optimized: 58 1.06 // [0.125 1.    1.    0.125 1.   ]\n",
+      "Optimized: 63 1.06 // [0.12598425 0.12598425 1.         0.12598425 1.        ]\n",
+      "Optimized: 70 1.06 // [0.12698413 0.12698413 1.         0.12698413 0.12698413]\n",
+      "Optimized: 75 1.06 // [0.128 1.    1.    1.064 1.   ]\n",
+      "Optimized: 76 1.06 // [1. 1. 1. 1. 1.]\n",
+      "Optimized: 82 1.07 // [0.1300813 1.        1.        0.1300813 0.1300813]\n",
+      "Optimized: 85 1.07 // [0.13114754 0.13114754 1.         0.13114754 1.06557377]\n",
+      "Optimized: 87 1.07 // [1.        0.1322314 1.        0.1322314 0.1322314]\n",
+      "Optimized: 90 1.07 // [0.13333333 0.13333333 1.         1.06666667 1.        ]\n",
+      "Optimized: 91 1.07 // [0.13445378 1.         1.         1.         0.13445378]\n",
+      "Optimized: 94 1.07 // [1.         0.13559322 1.         0.13559322 0.13559322]\n",
+      "Optimized: 99 1.07 // [1. 1. 1.]\n",
       "All values optimized.\n"
      ]
     }
@@ -188,18 +370,19 @@
     "    if current_db_object_count == 0:\n",
     "        print(\"No objects left to optimize.\")\n",
     "        if current_cache_size > 0:\n",
+    "            print(\"Add obj with optimized hitrate 0 and add them to optimization pool for re-optimization.\")\n",
     "            # Redistribute unused cache size among items with zero hit probability\n",
     "            differenc_set = np.where(optimized_hitrates == 0)[0]\n",
-    "            fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set)\n",
+    "            fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set).tolist()\n",
     "            current_db_object_count = len(differenc_set)\n",
     "            continue\n",
     "        else:\n",
+    "            \"Reset\"\n",
     "            optimized_hitrates[differenc_set] = 0\n",
     "            break\n",
     "    # Compute Lagrangian multiplier and optimal hit probabilities\n",
     "    eta = eta_star(current_db_object_count, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n",
     "    optimized_hitrates[differenc_set] = (c_f - eta / lambda_vals[differenc_set]) / c_delta\n",
-    "\n",
     "    if eta < 0:\n",
     "        print(\"eta was negative.\")\n",
     "        current_cache_size = current_db_object_count * c_f / c_delta  # Adjust cache size for next iteration\n",
@@ -210,18 +393,150 @@
     "        break\n",
     "    \n",
     "    max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
-    "    optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n",
-    "\n",
-    "    current_cache_size =- optimized_hitrates[max_outbound_index]\n",
     "    fix_i.append(max_outbound_index)\n",
     "    differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
-    "    current_db_object_count -= 1"
+    "\n",
+    "    old_hitrate = optimized_hitrates[max_outbound_index]\n",
+    "    optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n",
+    "    \n",
+    "    print(f\"Optimized: {max_outbound_index} {old_hitrate:.2f} // {optimized_hitrates[max_outbound_index-2:max_outbound_index+3]}\")\n",
+    "    \n",
+    "    current_db_object_count -= 1\n",
+    "    current_cache_size -= optimized_hitrates[max_outbound_index]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "f559ee7a-be2f-4076-b01c-f08950ad5a88",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.13793103, 1.        , 0.13793103, 0.13793103, 1.        ,\n",
+       "       0.13793103, 1.        , 0.13793103, 0.13793103, 0.13793103,\n",
+       "       1.        , 0.13793103, 0.13793103, 0.13793103, 1.        ,\n",
+       "       1.        , 0.13793103, 0.13793103, 1.        , 0.13793103,\n",
+       "       0.13793103, 0.13793103, 0.13793103, 1.        , 0.13793103,\n",
+       "       0.13793103, 0.13793103, 1.        , 0.13793103, 0.13793103,\n",
+       "       0.13793103, 1.        , 0.13793103, 1.        , 0.13793103,\n",
+       "       0.13793103, 0.13793103, 1.        , 1.        , 0.13793103,\n",
+       "       1.        , 1.        , 1.        , 0.13793103, 0.13793103,\n",
+       "       0.13793103, 1.        , 0.13793103, 0.13793103, 0.13793103,\n",
+       "       1.        , 1.        , 0.13793103, 0.13793103, 0.13793103,\n",
+       "       0.13793103, 0.13793103, 1.        , 1.        , 0.13793103,\n",
+       "       1.        , 0.13793103, 0.13793103, 1.        , 0.13793103,\n",
+       "       1.        , 0.13793103, 1.        , 0.13793103, 0.13793103,\n",
+       "       1.        , 0.13793103, 0.13793103, 0.13793103, 1.        ,\n",
+       "       1.        , 1.        , 1.        , 1.        , 0.13793103,\n",
+       "       0.13793103, 1.        , 1.        , 0.13793103, 0.13793103,\n",
+       "       1.        , 0.13793103, 1.        , 0.13793103, 0.13793103,\n",
+       "       1.        , 1.        , 1.        , 0.13793103, 1.        ,\n",
+       "       0.13793103, 0.13793103, 1.        , 1.        , 1.        ])"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "optimized_hitrates"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "8b2d3cea-1cc0-476e-92bf-2ac4344a9b1b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>0</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>count</th>\n",
+       "      <td>100.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>mean</th>\n",
+       "      <td>0.500000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>std</th>\n",
+       "      <td>0.427625</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>min</th>\n",
+       "      <td>0.137931</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>25%</th>\n",
+       "      <td>0.137931</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>50%</th>\n",
+       "      <td>0.137931</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>75%</th>\n",
+       "      <td>1.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>max</th>\n",
+       "      <td>1.000000</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                0\n",
+       "count  100.000000\n",
+       "mean     0.500000\n",
+       "std      0.427625\n",
+       "min      0.137931\n",
+       "25%      0.137931\n",
+       "50%      0.137931\n",
+       "75%      1.000000\n",
+       "max      1.000000"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pd.DataFrame(optimized_hitrates).describe()"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11682b36-e705-4bd9-9d75-79012791d1ee",
+   "id": "7a998837-72b8-4039-95a5-ca8d9c8e65ab",
    "metadata": {},
    "outputs": [],
    "source": []
diff --git a/01_nb_cncf_optimization/gen_nb_cost_optimization.ipynb b/01_nb_cncf_optimization/gen_nb_cost_optimization.ipynb
deleted file mode 100644
index 4675328..0000000
--- a/01_nb_cncf_optimization/gen_nb_cost_optimization.ipynb
+++ /dev/null
@@ -1,473 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "ab5cd7d1-1a57-46fc-8282-dae0a6cc2944",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "import numpy as np\n",
-    "import random"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "id": "3d1ad0b9-f6a8-4e98-84aa-6e02e4279954",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "DATABASE_OBJECT_COUNT = 100\n",
-    "CACHE_SIZE = DATABASE_OBJECT_COUNT/2\n",
-    "ZIPF_CONSTANT = 2\n",
-    "\n",
-    "CACHE_MISS_COST = 2\n",
-    "CACHE_REFRESH_COST = 1\n",
-    "\n",
-    "SEED = 42\n",
-    "np.random.seed(SEED)\n",
-    "random.seed(SEED)\n",
-    "\n",
-    "LAMBDA_VALUES = np.array([np.random.zipf(ZIPF_CONSTANT) for i in np.arange(1, DATABASE_OBJECT_COUNT + 1,1)])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "id": "9cc83cf6-5c78-4f0d-b7cb-08cdb80c362e",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# LAMBDA_VALUES = np.array([0.03, 0.04,0.05,0.06,0.07,1,1.1,1.2,1.3,1.4,1.5])\n",
-    "# DATABASE_OBJECT_COUNT = len(LAMBDA_VALUES)\n",
-    "# CACHE_SIZE = 4.4\n",
-    "# CACHE_MISS_COST = 7\n",
-    "# CACHE_REFRESH_COST = 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "id": "3dc07233-0b56-4fee-a93b-212836c18b42",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "db_object_count = DATABASE_OBJECT_COUNT\n",
-    "cache_sz = CACHE_SIZE\n",
-    "\n",
-    "lambda_vals = LAMBDA_VALUES\n",
-    "c_f = CACHE_MISS_COST\n",
-    "c_delta = CACHE_REFRESH_COST"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "5a27d416-8f98-4814-af9e-6c6bef95f4ef",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals):\n",
-    "    num = (db_object_count * c_f - cache_sz * c_delta)\n",
-    "    denom = np.sum(1.0/lambda_vals)\n",
-    "    return max(0, num/denom)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "id": "6276a9ce-f839-4fe6-90f2-2195cf065fc8",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def h_i_star(c_f, eta, lambda_vals, c_delta):\n",
-    "    optimized_hitrate = (c_f - (eta/lambda_vals)) / c_delta\n",
-    "    return optimized_hitrate"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "id": "dcd31a8c-6864-4b9a-8bb3-998f0c32baf6",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n",
-    "    local_hitrates = hitrates[(hitrates < 0) | (hitrates > 1)]\n",
-    "    smallest_delta = np.abs(np.min(local_hitrates))\n",
-    "    biggest_delta = np.max(local_hitrates) - 1\n",
-    "    if smallest_delta > biggest_delta:\n",
-    "        index = np.where(hitrates == np.min(local_hitrates))[0][0]\n",
-    "        return index\n",
-    "    else:\n",
-    "        index = np.where(hitrates == np.max(local_hitrates))[0][0]\n",
-    "        return index"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "id": "55b251f8-97ca-49a8-9ec6-be77dc1e49b2",
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [],
-   "source": [
-    "\"\"\"\n",
-    "Perform theoretical optimization to compute optimal hit probabilities.\n",
-    "\n",
-    "Parameters:\n",
-    "- lambda_vals (numpy array): Request rates for each item.\n",
-    "- B (float): Total cache size.\n",
-    "- c_f (float): Fetching linear cost (cache miss cost).\n",
-    "- c_delta (float): Age linear cost.\n",
-    "\n",
-    "Returns:\n",
-    "- h_opt (numpy array): Optimal hit probabilities for each item.\n",
-    "\"\"\"\n",
-    "optimized_hitrates = np.zeros(DATABASE_OBJECT_COUNT)\n",
-    "differenc_set = np.arange(DATABASE_OBJECT_COUNT)\n",
-    "fix_i = []\n",
-    "current_db_objects = DATABASE_OBJECT_COUNT\n",
-    "current_cache_size = CACHE_SIZE\n",
-    "\n",
-    "while True:\n",
-    "    if current_db_objects == 0:\n",
-    "        # Handle special case: no items left to optimize\n",
-    "        if current_cache_size > 0:\n",
-    "            # Redistribute unused cache size among items with zero hit probability\n",
-    "            differenc_set = np.where(optimized_hitrates == 0)[0]\n",
-    "            fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set)\n",
-    "            current_db_objects = len(differenc_set)\n",
-    "            continue\n",
-    "        else:\n",
-    "            optimized_hitrates[differenc_set] = 0\n",
-    "            break\n",
-    "    # Compute Lagrangian multiplier and optimal hit probabilities\n",
-    "    mu = max(0, (current_db_objects * c_f - current_cache_size * c_delta) / np.sum(1.0 / lambda_vals[differenc_set]))\n",
-    "    eta = eta_star(current_db_objects, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n",
-    "    assert(mu == eta)\n",
-    "    optimized_hitrates[differenc_set] = (c_f - mu / lambda_vals[differenc_set]) / c_delta\n",
-    "    # print(optimized_hitrates)\n",
-    "    # Handle the case where mu < 0\n",
-    "    if mu < 0:\n",
-    "        current_cache_size = current_db_objects * c_f / c_delta  # Adjust cache size for next iteration\n",
-    "        continue\n",
-    "    # Check for constraint violations\n",
-    "    larger_i = np.where(optimized_hitrates > 1)[0]  # h > 1\n",
-    "    smaller_i = np.where(optimized_hitrates < 0)[0]  # h < 0\n",
-    "    # If no violations, optimization is complete\n",
-    "    break_con = len(smaller_i) == 0 and len(larger_i) == 0\n",
-    "    break_con1 = len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0\n",
-    "    assert(break_con == break_con1)\n",
-    "    if break_con:\n",
-    "        break\n",
-    "    # Find the furthest violating item\n",
-    "    min_viol, min_viol_i = (0, -1)\n",
-    "    if len(smaller_i) > 0:\n",
-    "        min_viol_i = np.argmin(optimized_hitrates)\n",
-    "        min_viol = optimized_hitrates[min_viol_i]\n",
-    "    max_viol, max_viol_i = (0, -1)\n",
-    "    if len(larger_i) > 0:\n",
-    "        larger = optimized_hitrates - 1\n",
-    "        max_viol_i = np.argmax(larger)\n",
-    "        max_viol = larger[max_viol_i]\n",
-    "    # Compare the furthest violations and adjust accordingly\n",
-    "    viol_i = min_viol_i\n",
-    "    min_viol_flag = True  # True if furthest is from the left boundary\n",
-    "    if max_viol > abs(min_viol):\n",
-    "        viol_i = max_viol_i\n",
-    "        min_viol_flag = False    \n",
-    "    index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
-    "    if viol_i != index:\n",
-    "        print(optimized_hitrates[viol_i])\n",
-    "        print(optimized_hitrates[index])\n",
-    "        assert(viol_i == index)\n",
-    "    if min_viol_flag:\n",
-    "        optimized_hitrates[viol_i] = 0\n",
-    "    else:\n",
-    "        optimized_hitrates[viol_i] = min(1, current_cache_size)\n",
-    "\n",
-    "    # Update parameters for next iteration\n",
-    "    current_cache_size =- optimized_hitrates[viol_i]\n",
-    "    fix_i.append(viol_i)\n",
-    "    differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
-    "    current_db_objects = DATABASE_OBJECT_COUNT - len(fix_i)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "id": "efa16eaf-a10b-4927-99cd-190e2ffe1d1e",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "a = optimized_hitrates\n",
-    "b = differenc_set"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c",
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "All values optimized.\n"
-     ]
-    }
-   ],
-   "source": [
-    "\"\"\"\n",
-    "Perform theoretical optimization to compute optimal hit probabilities.\n",
-    "\n",
-    "Parameters:\n",
-    "- lambda_vals (numpy array): Request rates for each item.\n",
-    "- B (float): Total cache size.\n",
-    "- c_f (float): Fetching linear cost (cache miss cost).\n",
-    "- c_delta (float): Age linear cost.\n",
-    "\n",
-    "Returns:\n",
-    "- h_opt (numpy array): Optimal hit probabilities for each item.\n",
-    "\"\"\"\n",
-    "optimized_hitrates = np.zeros(DATABASE_OBJECT_COUNT)\n",
-    "differenc_set = np.arange(DATABASE_OBJECT_COUNT)\n",
-    "fix_i = []\n",
-    "current_db_objects = DATABASE_OBJECT_COUNT\n",
-    "current_cache_size = CACHE_SIZE\n",
-    "\n",
-    "while True:\n",
-    "    if current_db_objects == 0:\n",
-    "        # Handle special case: no items left to optimize\n",
-    "        if current_cache_size > 0:\n",
-    "            # Redistribute unused cache size among items with zero hit probability\n",
-    "            differenc_set = np.where(optimized_hitrates == 0)[0]\n",
-    "            fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set)\n",
-    "            current_db_objects = len(differenc_set)\n",
-    "            continue\n",
-    "        else:\n",
-    "            optimized_hitrates[differenc_set] = 0\n",
-    "            break\n",
-    "    # Compute Lagrangian multiplier and optimal hit probabilities\n",
-    "    eta = eta_star(current_db_objects, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n",
-    "    optimized_hitrates[differenc_set] = (c_f - eta / lambda_vals[differenc_set]) / c_delta\n",
-    "\n",
-    "    if mu < 0:\n",
-    "        current_cache_size = current_db_objects * c_f / c_delta  # Adjust cache size for next iteration\n",
-    "        continue\n",
-    "    \n",
-    "    if len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0:\n",
-    "        print(\"All values optimized.\")\n",
-    "        break\n",
-    "    max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
-    "    optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n",
-    "\n",
-    "    current_cache_size =- optimized_hitrates[max_outbound_index]\n",
-    "    fix_i.append(max_outbound_index)\n",
-    "    differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
-    "    current_db_objects = DATABASE_OBJECT_COUNT - len(fix_i)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "id": "4f64253f-b389-4be9-b403-08027d480121",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
-       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
-       "       0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.,\n",
-       "       1., 0., 0., 0., 0., 0., 1., 0., 0., 1., 0., 0., 0., 0., 1., 0., 1.,\n",
-       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.,\n",
-       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.])"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "optimized_hitrates"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "id": "17d818db-ec88-4c26-92af-6d74862525d9",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.43902439,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.43902439,  0.        ,  0.        ,\n",
-       "        0.        ,  0.04878049,  0.        ,  0.04878049,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        , -0.        ,  0.        ,\n",
-       "        0.04878049,  0.04878049,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.43902439,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "       -0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "       -0.        ,  0.        ,  1.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        , -0.        ,  0.        ,\n",
-       "        0.        ,  0.43902439,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
-       "        0.        ,  0.        ,  0.        ,  0.04878049,  0.        ])"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "a"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "id": "791b3f96-527a-489e-970e-c92ec950177f",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6, 27, 31, 33, 40, 41, 50, 81, 98])"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "b"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "id": "c22fa973-432a-4c05-89bf-2a6ea82ae3d2",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6, 27, 50, 81])"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "differenc_set"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "id": "898e1266-5aaa-46f4-ac0f-c7807ac2b6bb",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "db_object_count = DATABASE_OBJECT_COUNT\n",
-    "cache_sz = CACHE_SIZE\n",
-    "loop_lambda = lambda_vals\n",
-    "\n",
-    "non_optimized_values = np.arange(db_object_count)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "id": "8cc9b8a9-f7ae-48fc-adfb-ac4b7a4998f1",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "db_object_count = DATABASE_OBJECT_COUNT\n",
-    "cache_sz = CACHE_SIZE\n",
-    "loop_lambda = lambda_vals\n",
-    "\n",
-    "optimized_hitrate = np.zeros(db_object_count)\n",
-    "non_optimized_values = np.arange(db_object_count)\n",
-    "optimized_value = {}\n",
-    "\n",
-    "eta = eta_star(db_object_count, c_f, cache_sz, c_delta, loop_lambda[non_optimized_values])\n",
-    "optimized_hitrate[non_optimized_values] = h_i_star(c_f, eta, loop_lambda[non_optimized_values], c_delta)\n",
-    "\n",
-    "max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrate)\n",
-    "optimized_value[max_outbound_index] = (1 if optimized_hitrate[max_outbound_index] > 1 else 0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "id": "cbcf3592-fcf2-4f54-a3cd-761097c12972",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{67: 1}"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "optimized_value"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "db732331-1d09-45b7-915c-73daa270b5e2",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "graphs",
-   "language": "python",
-   "name": "graphs"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.7"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/01_nb_cncf_optimization/nb_cost_optimization.ipynb b/01_nb_cncf_optimization/nb_cost_optimization.ipynb
index 725cd1d..88de62d 100644
--- a/01_nb_cncf_optimization/nb_cost_optimization.ipynb
+++ b/01_nb_cncf_optimization/nb_cost_optimization.ipynb
@@ -9,7 +9,8 @@
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
-    "import random"
+    "import random\n",
+    "import pandas as pd"
    ]
   },
   {
@@ -23,7 +24,7 @@
     "CACHE_SIZE = DATABASE_OBJECT_COUNT/2\n",
     "ZIPF_CONSTANT = 2\n",
     "\n",
-    "CACHE_MISS_COST = 1\n",
+    "CACHE_MISS_COST = 2\n",
     "CACHE_REFRESH_COST = 1\n",
     "\n",
     "SEED = 42\n",
@@ -95,62 +96,201 @@
    "outputs": [],
    "source": [
     "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n",
-    "    local_hitrates = hitrates[(hitrates < 0) | (hitrates > 1)]\n",
-    "    smallest_delta = np.abs(np.min(local_hitrates))\n",
-    "    biggest_delta = np.max(local_hitrates) - 1\n",
+    "    lower_bound_violation =  hitrates[(hitrates < 0)]\n",
+    "    upper_bound_violation = hitrates[(hitrates > 1)]\n",
+    "    smallest_delta = np.abs(np.min(lower_bound_violation))\n",
+    "    biggest_delta = np.max(upper_bound_violation) - 1\n",
     "    if smallest_delta > biggest_delta:\n",
+    "        print(smallest_delta)\n",
     "        index = np.where(hitrates == np.min(local_hitrates))[0][0]\n",
     "        return index\n",
     "    else:\n",
+    "        \n",
     "        index = np.where(hitrates == np.max(local_hitrates))[0][0]\n",
     "        return index"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
-   "id": "ccd4b95d-1cdd-4c99-a22e-4b31338993cf",
+   "execution_count": 8,
+   "id": "9d774304-ae68-43b3-a76a-e970c06c5236",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n",
+    "    outside_bounds = (hitrates < 0) | (hitrates > 1)\n",
+    "    distances = np.where(outside_bounds, np.maximum(np.abs(hitrates - 0), np.abs(hitrates - 1)), -np.inf)\n",
+    "    index = np.argmax(distances)\n",
+    "    return index"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "19678083-15e1-439b-be8c-42033d501644",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([0.30256805, 0.76752268, 0.30256805, 0.30256805, 0.65128403,\n",
-       "       0.30256805, 0.86051361, 0.30256805, 0.30256805, 0.30256805,\n",
-       "       0.65128403, 0.30256805, 0.30256805, 0.30256805, 0.65128403,\n",
-       "       0.65128403, 0.30256805, 0.30256805, 0.76752268, 0.30256805,\n",
-       "       0.30256805, 0.30256805, 0.30256805, 0.65128403, 0.30256805,\n",
-       "       0.30256805, 0.30256805, 0.86051361, 0.30256805, 0.30256805,\n",
-       "       0.30256805, 0.82564201, 0.30256805, 0.82564201, 0.30256805,\n",
-       "       0.30256805, 0.30256805, 0.76752268, 0.91282101, 0.30256805,\n",
-       "       0.82564201, 0.82564201, 0.65128403, 0.30256805, 0.30256805,\n",
-       "       0.30256805, 0.93025681, 0.30256805, 0.30256805, 0.30256805,\n",
-       "       0.86051361, 0.92250756, 0.30256805, 0.30256805, 0.30256805,\n",
-       "       0.30256805, 0.30256805, 0.95897459, 0.65128403, 0.30256805,\n",
-       "       0.97317569, 0.30256805, 0.30256805, 0.65128403, 0.30256805,\n",
-       "       0.93025681, 0.30256805, 0.98989229, 0.30256805, 0.30256805,\n",
-       "       0.65128403, 0.30256805, 0.30256805, 0.30256805, 0.76752268,\n",
-       "       0.65128403, 0.65128403, 0.76752268, 0.95350454, 0.30256805,\n",
-       "       0.30256805, 0.86051361, 0.65128403, 0.30256805, 0.30256805,\n",
-       "       0.65128403, 0.30256805, 0.65128403, 0.30256805, 0.30256805,\n",
-       "       0.65128403, 0.65128403, 0.76752268, 0.30256805, 0.65128403,\n",
-       "       0.30256805, 0.30256805, 0.98115049, 0.82564201, 0.65128403])"
+       "array([ 1,  3,  1,  1,  2,  1,  5,  1,  1,  1,  2,  1,  1,  1,  2,  2,  1,\n",
+       "        1,  3,  1,  1,  1,  1,  2,  1,  1,  1,  5,  1,  1,  1,  4,  1,  4,\n",
+       "        1,  1,  1,  3,  8,  1,  4,  4,  2,  1,  1,  1, 10,  1,  1,  1,  5,\n",
+       "        9,  1,  1,  1,  1,  1, 17,  2,  1, 26,  1,  1,  2,  1, 10,  1, 69,\n",
+       "        1,  1,  2,  1,  1,  1,  3,  2,  2,  3, 15,  1,  1,  5,  2,  1,  1,\n",
+       "        2,  1,  2,  1,  1,  2,  2,  3,  1,  2,  1,  1, 37,  4,  2])"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "eta = eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals)\n",
-    "optimized_hitrates = (c_f - eta / lambda_vals) / c_delta\n",
+    "lambda_vals"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "ccd4b95d-1cdd-4c99-a22e-4b31338993cf",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2.1159070575516945\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([-0.11590706,  1.29469765, -0.11590706, -0.11590706,  0.94204647,\n",
+       "       -0.11590706, -0.11590706, -0.11590706, -0.11590706,  0.94204647,\n",
+       "       -0.11590706, -0.11590706, -0.11590706,  0.94204647,  0.94204647,\n",
+       "       -0.11590706, -0.11590706,  1.29469765, -0.11590706, -0.11590706,\n",
+       "       -0.11590706, -0.11590706,  0.94204647, -0.11590706, -0.11590706,\n",
+       "       -0.11590706, -0.11590706, -0.11590706, -0.11590706,  1.47102324,\n",
+       "       -0.11590706,  1.47102324, -0.11590706, -0.11590706, -0.11590706,\n",
+       "        1.29469765,  1.73551162, -0.11590706,  1.47102324,  1.47102324,\n",
+       "        0.94204647, -0.11590706, -0.11590706, -0.11590706,  1.78840929,\n",
+       "       -0.11590706, -0.11590706, -0.11590706,  1.76489922, -0.11590706,\n",
+       "       -0.11590706, -0.11590706, -0.11590706, -0.11590706,  1.87553488,\n",
+       "        0.94204647, -0.11590706,  1.91861896, -0.11590706, -0.11590706,\n",
+       "        0.94204647, -0.11590706,  1.78840929, -0.11590706,  1.96933468,\n",
+       "       -0.11590706, -0.11590706,  0.94204647, -0.11590706, -0.11590706,\n",
+       "       -0.11590706,  1.29469765,  0.94204647,  0.94204647,  1.29469765,\n",
+       "        1.85893953, -0.11590706, -0.11590706,  0.94204647, -0.11590706,\n",
+       "       -0.11590706,  0.94204647, -0.11590706,  0.94204647, -0.11590706,\n",
+       "       -0.11590706,  0.94204647,  0.94204647,  1.29469765, -0.11590706,\n",
+       "        0.94204647, -0.11590706, -0.11590706,  1.94281332,  1.47102324,\n",
+       "        0.94204647])"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "eta = eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals[lambda_vals != lambda_vals[6]])\n",
+    "print(eta)\n",
+    "optimized_hitrates = (c_f - eta / lambda_vals[lambda_vals != lambda_vals[6]]) / c_delta\n",
     "optimized_hitrates"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 11,
+   "id": "05b17074-719f-4bca-8434-2aaee26094d0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>0</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>count</th>\n",
+       "      <td>96.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>mean</th>\n",
+       "      <td>0.437500</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>std</th>\n",
+       "      <td>0.726101</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>min</th>\n",
+       "      <td>-0.115907</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>25%</th>\n",
+       "      <td>-0.115907</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>50%</th>\n",
+       "      <td>-0.115907</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>75%</th>\n",
+       "      <td>0.942046</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>max</th>\n",
+       "      <td>1.969335</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "               0\n",
+       "count  96.000000\n",
+       "mean    0.437500\n",
+       "std     0.726101\n",
+       "min    -0.115907\n",
+       "25%    -0.115907\n",
+       "50%    -0.115907\n",
+       "75%     0.942046\n",
+       "max     1.969335"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pd.DataFrame(optimized_hitrates).describe()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
    "id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c",
    "metadata": {
     "scrolled": true
@@ -160,6 +300,48 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "Optimized: 67 1.97 // [ 1.79077042 -0.09229584  1.         -0.09229584 -0.09229584]\n",
+      "Optimized: 97 1.94 // [-0.07876743 -0.07876743  1.          1.48030814  0.96061628]\n",
+      "Optimized: 60 1.92 // [ 0.96720258 -0.06559484  1.         -0.06559484 -0.06559484]\n",
+      "Optimized: 57 1.88 // [-0.05274002 -0.05274002  1.          0.97362999 -0.05274002]\n",
+      "Optimized: 78 1.86 // [ 0.97977406  1.31984937  1.         -0.04045188 -0.04045188]\n",
+      "Optimized: 46 1.80 // [-0.02836604 -0.02836604  1.         -0.02836604 -0.02836604]\n",
+      "Optimized: 65 1.80 // [ 0.99140044 -0.01719911  1.         -0.01719911  1.        ]\n",
+      "Optimized: 51 1.78 // [-0.00600086  1.59879983  1.         -0.00600086 -0.00600086]\n",
+      "Optimized: 38 1.75 // [0.00491746 1.33497249 1.         0.00491746 1.50122936]\n",
+      "Optimized: 6 1.60 // [1.00774103 0.01548205 1.         0.01548205 0.01548205]\n",
+      "Optimized: 27 1.60 // [0.02399435 0.02399435 1.         0.02399435 0.02399435]\n",
+      "Optimized: 50 1.61 // [0.03255485 0.03255485 1.         1.         0.03255485]\n",
+      "Optimized: 81 1.61 // [0.04116395 0.04116395 1.         1.02058197 0.04116395]\n",
+      "Optimized: 31 1.51 // [0.04982206 0.04982206 1.         0.04982206 1.51245552]\n",
+      "Optimized: 33 1.51 // [1.         0.05714286 1.         0.05714286 0.05714286]\n",
+      "Optimized: 40 1.52 // [1.         0.06451613 1.         1.51612903 1.03225806]\n",
+      "Optimized: 41 1.52 // [0.07194245 1.         1.         1.03597122 0.07194245]\n",
+      "Optimized: 98 1.52 // [0.07942238 1.         1.         1.03971119]\n",
+      "Optimized: 1 1.36 // []\n",
+      "Optimized: 18 1.36 // [0.09223301 0.09223301 1.         0.09223301 0.09223301]\n",
+      "Optimized: 37 1.37 // [0.09756098 0.09756098 1.         1.         0.09756098]\n",
+      "Optimized: 74 1.37 // [0.10294118 0.10294118 1.         1.05147059 1.05147059]\n",
+      "Optimized: 77 1.37 // [1.05418719 1.05418719 1.         1.         0.10837438]\n",
+      "Optimized: 92 1.37 // [1.05693069 1.05693069 1.         0.11386139 1.05693069]\n",
+      "Optimized: 4 1.06 // [0.11940299 0.11940299 1.         0.11940299 1.        ]\n",
+      "Optimized: 10 1.06 // [0.12030075 0.12030075 1.         0.12030075 0.12030075]\n",
+      "Optimized: 14 1.06 // [0.12121212 0.12121212 1.         1.06060606 0.12121212]\n",
+      "Optimized: 15 1.06 // [0.1221374 1.        1.        0.1221374 0.1221374]\n",
+      "Optimized: 23 1.06 // [0.12307692 0.12307692 1.         0.12307692 0.12307692]\n",
+      "Optimized: 42 1.06 // [1.         1.         1.         0.12403101 0.12403101]\n",
+      "Optimized: 58 1.06 // [0.125 1.    1.    0.125 1.   ]\n",
+      "Optimized: 63 1.06 // [0.12598425 0.12598425 1.         0.12598425 1.        ]\n",
+      "Optimized: 70 1.06 // [0.12698413 0.12698413 1.         0.12698413 0.12698413]\n",
+      "Optimized: 75 1.06 // [0.128 1.    1.    1.064 1.   ]\n",
+      "Optimized: 76 1.06 // [1. 1. 1. 1. 1.]\n",
+      "Optimized: 82 1.07 // [0.1300813 1.        1.        0.1300813 0.1300813]\n",
+      "Optimized: 85 1.07 // [0.13114754 0.13114754 1.         0.13114754 1.06557377]\n",
+      "Optimized: 87 1.07 // [1.        0.1322314 1.        0.1322314 0.1322314]\n",
+      "Optimized: 90 1.07 // [0.13333333 0.13333333 1.         1.06666667 1.        ]\n",
+      "Optimized: 91 1.07 // [0.13445378 1.         1.         1.         0.13445378]\n",
+      "Optimized: 94 1.07 // [1.         0.13559322 1.         0.13559322 0.13559322]\n",
+      "Optimized: 99 1.07 // [1. 1. 1.]\n",
       "All values optimized.\n"
      ]
     }
@@ -188,18 +370,19 @@
     "    if current_db_object_count == 0:\n",
     "        print(\"No objects left to optimize.\")\n",
     "        if current_cache_size > 0:\n",
+    "            print(\"Add obj with optimized hitrate 0 and add them to optimization pool for re-optimization.\")\n",
     "            # Redistribute unused cache size among items with zero hit probability\n",
     "            differenc_set = np.where(optimized_hitrates == 0)[0]\n",
-    "            fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set)\n",
+    "            fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set).tolist()\n",
     "            current_db_object_count = len(differenc_set)\n",
     "            continue\n",
     "        else:\n",
+    "            \"Reset\"\n",
     "            optimized_hitrates[differenc_set] = 0\n",
     "            break\n",
     "    # Compute Lagrangian multiplier and optimal hit probabilities\n",
     "    eta = eta_star(current_db_object_count, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n",
     "    optimized_hitrates[differenc_set] = (c_f - eta / lambda_vals[differenc_set]) / c_delta\n",
-    "\n",
     "    if eta < 0:\n",
     "        print(\"eta was negative.\")\n",
     "        current_cache_size = current_db_object_count * c_f / c_delta  # Adjust cache size for next iteration\n",
@@ -210,18 +393,150 @@
     "        break\n",
     "    \n",
     "    max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
-    "    optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n",
-    "\n",
-    "    current_cache_size =- optimized_hitrates[max_outbound_index]\n",
     "    fix_i.append(max_outbound_index)\n",
     "    differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
-    "    current_db_object_count -= 1"
+    "\n",
+    "    old_hitrate = optimized_hitrates[max_outbound_index]\n",
+    "    optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n",
+    "    \n",
+    "    print(f\"Optimized: {max_outbound_index} {old_hitrate:.2f} // {optimized_hitrates[max_outbound_index-2:max_outbound_index+3]}\")\n",
+    "    \n",
+    "    current_db_object_count -= 1\n",
+    "    current_cache_size -= optimized_hitrates[max_outbound_index]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "f559ee7a-be2f-4076-b01c-f08950ad5a88",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.13793103, 1.        , 0.13793103, 0.13793103, 1.        ,\n",
+       "       0.13793103, 1.        , 0.13793103, 0.13793103, 0.13793103,\n",
+       "       1.        , 0.13793103, 0.13793103, 0.13793103, 1.        ,\n",
+       "       1.        , 0.13793103, 0.13793103, 1.        , 0.13793103,\n",
+       "       0.13793103, 0.13793103, 0.13793103, 1.        , 0.13793103,\n",
+       "       0.13793103, 0.13793103, 1.        , 0.13793103, 0.13793103,\n",
+       "       0.13793103, 1.        , 0.13793103, 1.        , 0.13793103,\n",
+       "       0.13793103, 0.13793103, 1.        , 1.        , 0.13793103,\n",
+       "       1.        , 1.        , 1.        , 0.13793103, 0.13793103,\n",
+       "       0.13793103, 1.        , 0.13793103, 0.13793103, 0.13793103,\n",
+       "       1.        , 1.        , 0.13793103, 0.13793103, 0.13793103,\n",
+       "       0.13793103, 0.13793103, 1.        , 1.        , 0.13793103,\n",
+       "       1.        , 0.13793103, 0.13793103, 1.        , 0.13793103,\n",
+       "       1.        , 0.13793103, 1.        , 0.13793103, 0.13793103,\n",
+       "       1.        , 0.13793103, 0.13793103, 0.13793103, 1.        ,\n",
+       "       1.        , 1.        , 1.        , 1.        , 0.13793103,\n",
+       "       0.13793103, 1.        , 1.        , 0.13793103, 0.13793103,\n",
+       "       1.        , 0.13793103, 1.        , 0.13793103, 0.13793103,\n",
+       "       1.        , 1.        , 1.        , 0.13793103, 1.        ,\n",
+       "       0.13793103, 0.13793103, 1.        , 1.        , 1.        ])"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "optimized_hitrates"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "8b2d3cea-1cc0-476e-92bf-2ac4344a9b1b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
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+       "        vertical-align: middle;\n",
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+       "\n",
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+       "  <thead>\n",
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+       "      <th></th>\n",
+       "      <th>0</th>\n",
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+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>count</th>\n",
+       "      <td>100.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>mean</th>\n",
+       "      <td>0.500000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>std</th>\n",
+       "      <td>0.427625</td>\n",
+       "    </tr>\n",
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+       "      <th>min</th>\n",
+       "      <td>0.137931</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>25%</th>\n",
+       "      <td>0.137931</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>50%</th>\n",
+       "      <td>0.137931</td>\n",
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+       "      <th>75%</th>\n",
+       "      <td>1.000000</td>\n",
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+       "      <th>max</th>\n",
+       "      <td>1.000000</td>\n",
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+       "  </tbody>\n",
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+      ],
+      "text/plain": [
+       "                0\n",
+       "count  100.000000\n",
+       "mean     0.500000\n",
+       "std      0.427625\n",
+       "min      0.137931\n",
+       "25%      0.137931\n",
+       "50%      0.137931\n",
+       "75%      1.000000\n",
+       "max      1.000000"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pd.DataFrame(optimized_hitrates).describe()"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11682b36-e705-4bd9-9d75-79012791d1ee",
+   "id": "7a998837-72b8-4039-95a5-ca8d9c8e65ab",
    "metadata": {},
    "outputs": [],
    "source": []