Solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "10fa39c4",
   "metadata": {},
   "source": [
    "# Online Math Olympiad Apple Tree Probability Computational Solution\n",
    "This notebook is a computational approximate solution to the \"Apple Tree Probability\" problem stated in MindYourDecisions video, https://www.youtube.com/watch?v=RY7YKSw1t_M."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "af055294",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Needed libraries: random seeds growing, plots and stylized plots\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# from jupyterthemes import jtplot\n",
    "# jtplot.style(theme='onedork', context='notebook', ticks=True, grid=False)\n",
    "plt.rcParams['figure.dpi'] = 100\n",
    "plt.rcParams['savefig.dpi'] = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "40680381",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "# 1 experiment with 6 seeds\n",
    "seeds = 6\n",
    "days = 0\n",
    "# While not all seeds have grown, continue\n",
    "while seeds > 0:\n",
    "    # Iteration through every day\n",
    "    days += 1\n",
    "    for seed in range(0, seeds):\n",
    "        # If random value in range [0,1] is bigger than 0.5, seed grows\n",
    "        if random.random() > 0.5:\n",
    "            # Seed is a tree now, amount of seeds left is 1 less\n",
    "            seeds -= 1\n",
    "print(days)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "720ce7c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.03274\n"
     ]
    }
   ],
   "source": [
    "# Calculate amount average amount of days, using [length] experiments\n",
    "days = 0\n",
    "# Do 100000 experiments\n",
    "length = 100000\n",
    "for k in range(0, length):\n",
    "    seeds = 6\n",
    "    while seeds > 0:\n",
    "        days+=1\n",
    "        for seed in range(0, seeds):\n",
    "            if random.random() > 0.5:\n",
    "                seeds -= 1\n",
    "# Calculate the average amount of days\n",
    "days = days/length\n",
    "print(days)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e0dc3462",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Seeds[ 0 ]:  1\n",
      "Seeds[ 1 ]:  2\n",
      "Seeds[ 2 ]:  4\n",
      "Seeds[ 3 ]:  8\n",
      "Seeds[ 4 ]:  16\n",
      "Seeds[ 5 ]:  32\n",
      "Seeds[ 6 ]:  64\n",
      "Seeds[ 7 ]:  128\n",
      "Seeds[ 8 ]:  256\n",
      "Seeds[ 9 ]:  512\n",
      "Seeds[ 10 ]:  1024\n",
      "Seeds[ 11 ]:  2048\n",
      "Seeds[ 12 ]:  4096\n",
      "Seeds[ 13 ]:  8192\n",
      "Seeds[ 14 ]:  16384\n",
      "Seeds[ 15 ]:  32768\n",
      "Seeds[ 16 ]:  65536\n",
      "Seeds[ 17 ]:  131072\n",
      "Seeds[ 18 ]:  262144\n",
      "Seeds[ 19 ]:  524288\n",
      "[2.36, 2.48, 3.69, 4.52, 5.31, 6.24, 7.33, 8.31, 9.52, 10.24, 11.58, 12.43, 13.46, 14.64, 15.64, 16.5, 17.38, 18.25, 19.62, 20.26]\n"
     ]
    }
   ],
   "source": [
    "# Calculate average amount of days for different amount of seeds\n",
    "res = []\n",
    "seedVal = 1\n",
    "accuracy = 100\n",
    "for j in range(0, 20):\n",
    "    print(\"Seeds[\",j,\"]: \", seedVal)\n",
    "    days = 0\n",
    "    for k in range(0, accuracy):\n",
    "        seeds = seedVal\n",
    "        while seeds > 0:\n",
    "            days += 1\n",
    "            for seed in range(0, seeds):\n",
    "                if random.random() > 0.5:\n",
    "                    seeds -= 1\n",
    "    days = days / accuracy\n",
    "    res += [days]\n",
    "    # Increase seed amount\n",
    "    seedVal *= 2\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "05b3266c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the dependancy\n",
    "seedVals = 2**np.arange(len(res))\n",
    "plt.plot(seedVals, res)\n",
    "plt.plot(seedVals, np.log2(seedVals)+1.4)\n",
    "plt.xlabel('SeedAmount, N')\n",
    "plt.ylabel('AmountOfDays, E')\n",
    "plt.title('E(N)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c0cd1ce",
   "metadata": {},
   "source": [
    "We can see that the graph looks very same with function E(N) = log2(N) + a, where a is approximately 1.4 (could be sqrt(2) possibly)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "33719826",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}