genetic_algorithm.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "dotnet_interactive": {
     "language": "csharp"
    }
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import matplotlib.pylab as pyl\n",
    "import math\n",
    "from scipy.optimize import root_scalar, RootResults"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "dotnet_interactive": {
     "language": "csharp"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x22ad4c456f0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZPYLOMJjV5KN2h4NUQwQ7rO1r9dCQgOpiHkkkT2sMEaohLQzFFhryzl1gaUMNiGvX4AwLZZpOBnQZTtnOPnNisKF5quQREMwwh4Y41Cy8SIwzFIBO1RBraEigaohlLoDEIbPVji1iHkFIOIdHYMGCMl1OTfJRghXZwdpryHuDEhUaUhRGj0Bh7zWkq4ZMDA0B3psby3nWu7RyqIZEdR9lmUUAdKsstlCymDcXNBBkCL7j6Dpzxlg7IC40xOoRaE/zLLJXXTVkYmgI8IaHWJ7M5c7QEHtBmRiPwKsaojoCX+H1/Ab8/IB8KhE0SBxPEvoNVZRHwJEA1T7DKLpqyMTQEKAVdhm/sXVVYDOG0QTIR2WHA7LdzuwRWFE+Kjv4CgcHggzBdxztaY/lpjpYcwRaWIclYayrhkwsKNOOxxQacvAXlEkmxtptNhtunJ0BAGj79lumz1AsWFCmh4YCdF1a50xaFJ4BL0ILyjhCQypHSEtXDZnsEQgLDSlu00JDF4+5HLN+txiJ134fFdtc2PVxMdPnWLGOgKf3li+QIfiOw+NSim4xwXxz4whpiSgoA9hDNLw3CDN6DTnDQjFt4X3413l3o/X0Gbz16FPY9WEh8+dZMVnM21NqIKxzJi2KFnfmqiwWkCPgGdTt6VQbMckxBRSUARyhIV7VUICnfX1v8g244/HfICr+EmzfkI8PX1iBs6dOc32mniOwoHyUtV5kIKxzJi2KzNPXX6BqiLU/EsBXES2ioAzQQkMMyWLO0BBPp9YLMSw6CjMXP4Trpk9FY/UhrLj3P1Fdstsvn02qIf9jnTNpUXhCBx6OildeWDumAnwV0SIKygD2EA2vaohnmtv5sNlsuGH2TPz7Qz+H3elAwUuv4pPX/4/ZYzkfXZXF1rl98X7PA2GdM2lR9J49LKohoU3nODwCnt49AtpQa8djCcF1VZwyDq9X/Bcaik2+HLNzvMngym078c6zf8Dxw7V++ezuWDFHwNON1xescyYtin4BcYSGbEJUQ+w5Ap7chog21NrxmDwCPxSU8XoEjtAQpC28D/867ydoPXMGax9dipIP/8b1mRfCknUEAZaP+uVRLz09HeXl5aisrMTixYv7/N7pdCIvLw+VlZXYtm0bEhISAAAJCQk4e/YsSktLUVpaipdfftkfyyG6wVOa3hViEeMRsEsiNbUTR0HZoFENsXt8+nE5Qn+J134fv3lvLW6ePw87PyjA8tszA2oEAGvWEQS9akiSJKxYsQLTpk1DXV0dXC4X8vPzsX//fn2b+fPno6WlBcnJybjrrruwfPlyZGZmAgAOHjyIlJQU3mWYgjMsFI9+tB71Byrx0QsrcKzioOglDQjPBaQXlImoLOYpKNOauDHc4ESqhlhuyHobajfHhDKOG+ptj/wCdocDK376c1TvLGX+HCMMtmTx8JHRSPv5fFz/ozT8z38sQEOl8ftGoFVD3H/hqampqKqqQk1NDTo6OpCXl4eMjIwe22RkZGD16tUAgHfeeQe33HIL72GFMCQyAsNHRmPs5Bvx8Po1uPu/fofIi2NFL+uC8LiUXT17BldBGU+vIZsg1ZBHUZiS21obaqWD3WjyhIbCRwxHze4vTTMCQPccQXAXlIUMCcf0RQuw5MN1uHHWTISEh2Nkwmimzwr6XkNxcXGore1KCNXV1SEuLq7fbRRFwalTpxAVFQUASEpKwq5du7B161ZMnjy53+NkZ2fD5XLB5XIhOjqad9lMOMPCAADrn16Ov7+xFtem34wlH76N2379C4SPGC5kTQMhcbSY6JKPDrKCMg5PRpxHwJgj4OxKydtrKGRIONq+YWsVwYqqqqa3xjCCbLdj8k9m4bGP38G0+3+Kr7Z+ilcWPAig6x7C8plAEIeGeDh27BguvfRSnDhxAtdffz3ef/99XH311Thz5kyfbXNzc5GbmwsAcLlcZi8VAOAMDQUAnGpowrb17+OzteuRvigbN83LxMQ7bsPmlWvw6Vvr4W5rE7K+89GlNmAZAi8wNMRVUOYP1ZAAj4AnNMRcUMYXGgoZEo5zjANmeFACXAjHgk2ScN30qZj+QDaiL41H5fad+PD5FagrK8ewaO+Dr3YPMUqgVUPcf+H19fUYPbrL3YmPj0d9fX2/28iyjBEjRqC5uRnt7e04ceIEAGDXrl04ePAgxowZw7ukgOEI836J7ee8AzVONjbh7Sf/C3+eNQ/Vu/bg1l89gEc/Wocb5/w4aC7Srl5Dxi8gzXgICQ057ExKJ4CvEM4mSDXkDQ0Z/3PUhtfzzCwG2GpFbDYbQocMQdu3ZAi+f8u/4tfvrMF/LF+K9tZW5P7nr/CXn/0CdWXlAICOznuGIyyE6fN5CkN9gdsQuFwuJCcnIzExEQ6HA5mZmcjPz++xTX5+PrKysgAAs2bNwpYtWwAA0dHR+sWflJSE5ORkVFdX8y4pYDg7DYH2pWo0VB7E67/4DVb89OdoqT+GWU/+Fos/eBupM28V0rCtOzJPslhvOifKI2AfVQmwVhaLrCNg8Agc3lyKqqpMx9WlmAxVzc5wb5jD7NAQIG7Wcm++N+VGPPT2Ktz738sg2+1Y88gTeH52Fso/29ZjO+3h8TsbGlIUBYsWLUJhYSFkWcbrr7+OsrIyLF26FDt37sQHH3yAlStX4s0330RlZSVOnDihK4ZuuukmPP300+jo6IDH48HChQvR0tLC/T8VKDS3rr8Re9U7S/FS1kJcOekGTF+UjbueeRw3/2weiv6yEqUfF5v+lAl0TzKx1BGILCjzg2qIq9eQ+R6BI9T40yLPbGegq/hOtstwG4xohgwZAgDCQkMi6wiuSB2HGb+4H4nXfR/NdfVY+9jTKP24qN9r1uNW4O7oYA4N8RSG+oJfzmRBQQEKCgp6vJeTk6P/u62tDXPmzOmz37vvvot3333XH0swBUdoz9BQfxz4fBsOfL4NV/9wMqYvWoC5v38Kk++ejRVZCwNm0fvDH3UEYgrK7OxtEzgK4Qabakh2OLiuqa58ivFbQeiQcABiPAKRoaE5Tz2KiXfejpMNjVi/dBl2vP+hT/msjtZzTMYeoF5DQYUeGvJx6PZXWz9D2d8/x/RFCzB1wb0YETMSJ+qPBXKJfdBiv0zJYpGqITt7aIinEE7zIgaTaojn5sDT21/3CETkCDrEGYJr02/Bl5u24q3FOXC3t/u8X/u5cwgJ0tAQTSgzwEChofOhqiqOVlQB6PIozITPIxCrGmJOFrvZ163lFYR4BAw3Y29oiL2hW1eymMMjEBAa8rjdupLGTCRZRujQITh6oNKQEQC89w1NcGIUMgRBhJYc6zAoD9UMB2uiiAf9AmK4qeoewSCbUNZlwNgnlInIETB5MA4+j0DPETCcqxALhobChg0FALSe7itxH4iOc+f0qIJRNKMXtKohK+EMDYG7vd3wl9He2qrvbzZ6kmmQ5Qh4CspUjl5DQltMCAwNsRxbaGhIlCEYPgwAmyFoP3eOPVlMHkHw4AgNNRQW0ujSEIsLDbHNIxCsGmJNFnOEtLS2FIMrNMSfLGYJs+ihIcYh9DwoHW4hlcVhw7yG4CyLIWg9xxwe1nNXAZpHQIbAAM6wsAEVQ+ej/Zw3lMT6NMBDV46AJzQkYFSlg2dCGUdoSBYYGmJsQ83lEXCcKy00RB6Bb3S0soeGJE6DP+DnB+yTv4M4Q0PQfrbV8H56aEhAjqBLNcQRGhIxqpKr1xB7bkNcQZkY1ZCHMzSkuN1CWqqIMgThuiEwPne5vbWVvcUE5/c8EGQIDOAIC0XHOeMXvSY3ZdUQ88ATWxRVUGaz2SBJEvPNWOWQj+qqoUHiEYQOHcKlGuIZ+xg6JFxIewmgUzUkxCPwNpdsPfON4X3bz7VxqYbIEAQJ7KGhTtWQwNAQy41NVIsJiSOcBXTd3LhUQwJyBEaUOyHh4bjnj8/gsnHX4dDuvVzHBdh6DYUMCcc5AfkBgH+gDitaaIglR8CrGgqkl0oFZQZwhoYyaaY1L0KTn5qJJMvsnSk51Dc8yBzhLICva6o+vF5AryFfeyPFXJ6ErOefw8iE0fjov/8Xn7z+f+zH5QwNifIIxOUIhqKjrY0pHMYTGpLs7KFSXyBDYABHaAi+6eyWagSPosDd3i5EPsqjKhFVUKYnbDm7jzLJR4O86VzKj9IwO2cJ2ltb8ZfsB3HQtYvruFqyeLCFhkRVFocNH8aUKAa8oSG708nUR0u225kr7X2BDIEBvKEhtsRY+zl26RgPPCMfRbWY6JqqZn5rZUmWTVcMAZ3dNC/Q70d2OJDx219iUuadqC7ZjTd/8yROf33cL8cFGD2C8HCc+8Z4rNwfiMoRhA8fzpQfAHrmCo0aUB7xhC+QITCAMzSUSTUEeDXEoiqLmds5qyo8Ho/pBWVdU9U46wiYRlVKptcQAN4n8/5CQ5EXx+KePz2LhGuuxtY31uKjF//Xb3pyvaCMJUcwdAhONjb5ZR1GUdyKkO6jPB5Bm15YGmrYEPDWiwwEGQIDOMJCmJLFQKeGWFRoiONJQlU8pnsEkj6Eg6+ymHVUpdlVxYA3MX++p/IrJ92Aucuegmy3442HlmDv5r/79bjaOR50oSFBvYbChg3FmWbj4WGgK1fIohwKtGqIDIEBnGFhTPJRgK/hFA88ff0B79O12TmCrtAQo2qIo7WyJMmmK4YAb6hDkiTYbDaoqgqbJCFt4X2Yev9P0VBVjdW/ehTHj9T5/7g8BWXhYlVDonIETTWHmfblGU7j9exJNSQcyS7D7nDoxWFGaT8nLjTE16/eY7pqSA8NcfYaYq0jEDFAqHuFb+jQIZi77ClcOekGuDZ+jA3P/oH5AWTA43aGG1ibzlmtjiB8+HD2ZDFHzzHJYYfC6CH7AhkCH3GEeL885tCQMEMgc8UWvSELQaohzl5DrKMqRYWGACAx5Rr85LnfYUhkBNY99Xts35A/wJ586B6BwTCLMywUkiwL6TMEiKkjsNlsCB021A/JYrbQEHkEQYB2E+9oZQ0NtWJIZIQfV+QbEkc7Z0ALDZlcR+Bgb50NdFPCMHUflYUki7U13//qizjZ0ISX5t2PurIDgT8u41jPkPDOPkPfWKeOIGToEEiShLMM7SWAbj3HGB4ISTUUJHQNpWENDbWJ8wh4k8WCVEPcE8oYnhhtkiREPqrNuCj/bBv++vjTzOEHo7C2oQ4Z6m1B3XbWOjkCnlkEQPeeY2wegdE5KEYgQ+AjznDf5hX3h1c1JKKOgDNH4PHorZnNQkvysnoEPL2GeHoc8VDyUSFONjahbOtnUFXVtON21REYuxV0taAWlCPocEOSZT25bgbhWp8hRkPQoSeL2QxBIBPz1GvIR7S4XgejIWhrbYUjTIB8lFc1xDg5SyNqdDyGRUcZ2oendbaG4naz5QhkWUiy+NyZb/DVJ5+aagSA7vMIjHkEWvO1cwKmkwHd+kmZ6BXw9BkC+HqOyXY7PFRHIB6WecXd6RAUGuL1CPrTt/uCzWbDw+vfQOiQIajfX4H9n32B8s++wOE9+y5onHhaZ2uoHg+TEsYmSULko6LoCg0NfCu4eMwV+N6kibjyBzcgady1AMCsqedFWzfvzGYj8MwiAID2s+zJYsnOPsPbF8gQ+Ih2E2c1BO3nzsHucHhbPgQw+98b/glW7KEh2elE6JAhqHLtgs1mw7/9dC6mZmeh9fQZVGxzoeKLHajaUdJHHy9z9hrqWjfbqEoRqiFRXKiOYOhFkUi+YQKu/MFEXPmDVAwfGQ0AOFZ5EJ/+3zrs3byVWVPPi24IHHaALW3nMxGxMYi5LBH/cvNNADhCQ21asphVNUQegXA07S9zsrhzP0dICNrc5sVVJbvMHM4C+ArKNMntvs1/x6dvrUPo0CFIvmECxk6+EVdOvgHXpt0MADjZ2ISqHSU4uGMXqlwlXW2oBRTCSYJaTIii+zyCYVEX4fLxKbhsfAouH5+C2CsuAwB8e/IUKr7YgQP/3I4D/9yB001fi1wygC4hgb8SxjZJwkVxlyD28kTEXJ6EUUmJiLk8EaOSEhDaOZsZ8BrBM8ebmY6hejzeyABLaMhBlcVBgVYVzFrYo8lOnWFhpibYvAVl7DdUnhYTjhAnAKCjvR2AN568d9NW7N20FQAwMvFSXDFhHK5IvR5X/mAixt82A0DX0A/eWbwsIS2boKZzotBuqLdkz8OPfrkQAHDu229RU/olSj78Gyq3l6CurFxI3uRCdPVI8v0WJskyIi6OQfToOETFxyNqdByiL/X+d2TCaP3BBQBONX6NxuoauN7/CI0HD6Gx5hAaKg/i7Ck26ahG+zm2DgMkHw0S9NAQ49N1e7eGU2bCXVnM0XTOrhmCfozn14eO4OtDR/DF+vcAePvsX5E6Dpddfy1GxIxCc10926LBLnsVpRoShaqq2FO0BXanE9U7S3FwZynqyyuC/hxo17S9WyGcZJcxYuRIRMSOQsTFsYiIHYXIi2MRFR+HqNFxuOiSi3v0J+poa0Nz3VE019bjwOfb0Vhdg8bqQ2iqPhSwJDjrcBrqNRQkcIeGOg2I2f2GuHsNcaiGHE6vIXB3egQD0XiwBo0Ha/D5X99hOl53WGWvkqAWEyJZ8+vHRS/BMNpN8Y4nfoOwYUMRERuD4dFRfYz/2dOn0Vxbj/r9B7CnaAuaa+vRXFuH47V1ON103HSVVjujjHxQVBanp6fjxRdfhCzLeO2117B8+fIev3c6nVizZg3GjRuH5uZm3HXXXTh82JtkWrJkCebPnw9FUfDggw+iqKjIH0vyO1qm393m202tN7qG2OQOpNzdRzlaTGgzmkUMN/f292dRDYlpOkcYo6n6EM40n0BU3CU42diEii924OSxRpxsaMTJhia0HGvAyYYm5ge3QNHeyjaXhFf9NxDchkCSJKxYsQLTpk1DXV0dXC4X8vPzsX//fn2b+fPno6WlBcnJybjrrruwfPlyZGZmYuzYscjMzMTVV1+NSy65BJs2bcKYMWOCMkbrDAtDe+s55icITW1ktoRU8otqiDE05PQagg5G48mDx+P76MfuWE01NFipKzuAp37476KXYRie0FBQewSpqamoqqpCTU0NACAvLw8ZGRk9DEFGRgaeeuopAMA777yDl156SX8/Ly8P7e3tOHToEKqqqpCamopt27bxLqtf7CEhGH/7DMPuWcI1V3M9XbRzNJziQeaYUAZoSVfOZLEIj0DxsPUasphqiDCX9tZWjExMwE33ZBraz+50BLdHEBcXh9raWv11XV0dJk6c2O82iqLg1KlTiIqKQlxcXI+bfl1dHeLi4s57nOzsbCxYsAAAEB0dzbze5InjMft3i5n2rSn9kvm4POXlPPC3mGDPEdhDtNCQAI9AUdh6DVlMNUSYS9OhI7hy0g3I+O0vDe/bXOv/eRQagyZZnJubi9zcXACAy+Vi/hztRvzi3J+hqfqQoX1Zi8m672u2IZBlmasQRVXYVUO95aNmonrYZK+i2lAT1uD9ZS/gby+9ang/1aOi7WzgZOfchqC+vh6jR4/WX8fHx6O+vv6829TX10OWZYwYMQLNzc0+7etv5M6nxLOnTpvaJ4Wnzwgr4SOGQ3Y6uErTPRwtJgaSjwYSj6IwqYZsMoWGiMAiqj/TheA2BC6XC8nJyUhMTER9fT0yMzPxk5/8pMc2+fn5yMrKwrZt2zBr1ixs2bJFf3/t2rV4/vnncckllyA5ORk7duzgXdIF0XqqBLJc+3xooSF/5Qhkux0jYkchMjYGERfHIvKSWETGxiDy4hhEXnIxImJjdO+jjePC8ygKc/WmVqDjbhdjCNjqCGR0BLC5F0EEI9yGQFEULFq0CIWFhZBlGa+//jrKysqwdOlS7Ny5Ex988AFWrlyJN998E5WVlThx4gQyM72JkrKyMqxbtw5lZWVwu9144IEHAh6flf3Q0IyFjnPG+4w4QkMQNToe0aPjEX1pPKITuv49ImZUn9DH6ePNOHmsEccqD6LsH5/jZEMTTjU24cDn25nXzdN0TgsNickRsBeUqUFeTEUQ/sYvOYKCggIUFBT0eC8nJ0f/d1tbG+bMmXPefZ977jk899xz/liGT2gl6WYbAlVV+y0mGT4yGrFXJCHmsiTEXJGEUYkJiB4djxExI3ts982JFhw/UoeDrlI019V7tdLHGnXNtK+FW0bgaTrXJR8V4BEw9hqyyWIG0xCESAZNsthf+KPXPSvtra2IuSIJU+bOQcwVSYjtvPFrAy8Ab4OvpprDqNi2A18frkXzEW8V5PHaepxjnJXKA0/TOS1H4G43p01wd1groiUqKCMsiGUNgdkeAeBNUF910yRcddMkfHvyFBoOVmN3wSY0VtegoaoGDQer8U1zi+nruhAqox4f8OYIlA63kL413l5Dxi9vb4sJCg0R1sJ6hkAbjC7AI3jjV49ieHQUGqqqhQ30MIq36Rx7QVmHgEQxwL5uqw2mIQjAgoaAdzA6D1pTtcEET9M5u9MpRDoKdPYacrB4BFRQRlgPy80slv0w9MRKcKmGQkMCksD2BY+HrbKYVEOEFbGcIZDsdrhNmnH6XYC1nTPgbUMtQjoKdBbCGcxtyHY7nGFh5BEQlsNyhiDQXfy+a/A0nbOHhAiRjgLe0JCRHMGImJH4+ar/xYiYkagu2R24hRFEEGK5HEGgJ/1811A5PAJ7iFNIC2oAUD2+zyNIvmEC5i57Co7QELz5yBPYXbg5wKsjiODCeobAYReSKB6ssFboAl75qLAcgQ+FcDabDbdkZyH9gWw0VR/C6ocfQ1PNYZNWSBDBg+UMgWQP7BDo7xq8oypbBRTBAQM3ywsbPhw/+f3vcNVNk7Dro0KsX7o86KZZEYRZWM4QyDKFhozA2sUT8IaG3M2CcgQXaDoXf9X3kPX8cxg+Khobnv0j/vn2uyavjiCCC8sZAvIIjKF6PFzdR0XlCPpLct84+8eYueQhnGk+gRVZC3Fkb5mA1RFEcGE5Q0CqIWNwNZ0LcQpTDfVOcjvDQnHnk7/F+NtmoPyzbVj76FP49uQpIWsjiGDDkoaAPALf4Wk65wgJEVdH4O4KDY1MvBRZzz+HmMuTULgiF8WvvgGVagUIQseShoA8At/haTpndzqFjKkEupLF10z7N9z19ONQOjrw2n8+jAP/ZJ/NQBDfVSxnCCQHeQRG4Go6FyrQI1AUDL0oElnPP4fDe/ZhzSNP4GRDo5C1EESwYzlDIMuULDaCx8MmH7VJEuwOh7AcQce5NkiShM/Wrkf+H/+HvnOCuACWMwQS5QgMoTIWlNmdDgCAW5Ah2PrGW/hq66fULoIgfMByhkC224U9pQ5GtAZsNkkylGDVBteLko+eaT4xaGY+EIRoLNl0jjwC39HadRsND9lDxM0rJgjCGJY0BJ4OMgS+onkBNoPhIYezc16xII+AIAjfsZwhoMpiY2hjG417BF5DIEo+ShCE71jOEFBoyBiezkHuRovK9ByBoFGVBEH4juUMAXkExlAVLVlsMDTU6RGIakNNEITvWM4QUGWxMTTVkFGPQEsWi5KPEgThO5Y0BIpCHoGvaEbTaI5AtHyUIAjfsaQhII/Ad/Qcgd1YaEhPFpNHQBBBj+UMgWS3QyH5qM+oumqI5KME8V2FyxBERkaiqKgIFRUVKCoqQkRExHm3mzdvHioqKlBRUYF58+bp73/yyScoLy9HaWkpSktLMXLkSJ7l+ASphoyhVxYbzhGQfJQgBgtchmDJkiXYvHkzxowZg82bN2PJkiV9tomMjEROTg4mTpyI1NRU5OTk9DAYc+fORUpKClJSUvD111/zLMcnSDVkDD00xJojIPkoQQQ9XIYgIyMDq1evBgCsXr0aM2fO7LNNeno6iouL0dLSgpMnT6K4uBjTp0/nOSwXdocDHjIEPqOHhoxWFuvyUTIEBBHscBmCmJgYNDQ0AAAaGhoQExPTZ5u4uDjU1tbqr+vq6hAXF6e/XrVqFUpLS/HEE09c8FjZ2dlwuVxwuVyIjo5mWq92M1MUShb7Svemc0boko9SaIgggp0Bu48WFxcjNja2z/uPP/54n/dUVTV08Llz5+Lo0aMYOnQoNmzYgHvuuQdvvvnmebfNzc1Fbm4uAMDlchk6jobUOYSdPALf0ZvOGcgRpPwoDZMy78Tpr48bviYIgjCfAQ3BtGnT+v1dY2MjYmNj0dDQgNjYWDQ1NfXZpr6+Hj/84Q/11/Hx8di6dSsA4OjRowCAb775BmvXrkVqamq/hsAfyJ0SSFIN+Y7WdM4X1VBUfBzufPI3uPIHE3H4y6+wfunvA708giD8AFdoKD8/H1lZWQCArKwsbNy4sc82hYWFSEtLQ0REBCIiIpCWlobCwkLIsoyoqCgAgN1ux6233op9+/bxLGdA5E6PgJLFvuNRBg4NyXY7bvlZFn7z3ltIuOZf8O5//Qn/754FOFZx0KxlEgTBAddgmmXLlmHdunWYP38+Dh8+jDlz5gAAxo0bh4ULFyI7OxstLS145pln9HDO008/jZaWFoSHh6OwsBAOhwOyLGPTpk166CdQaEVRZAh8Z6Cmc0kp12DW7xYj9orLsKdoC95f9gJOf33czCUSBMEJlyE4ceIEpk6d2uf9kpISZGdn669XrVqFVatW9djm7NmzGD9+PM/hDSNTjsAw/RWUhQ0fhn//1c9x46yZOHH0GF574BHs/8fnIpZIEAQnlhpVqRsCUg35zPkKylJmTEPG4ocQPmI4Pln1Fopefg3tredELZEgCE4sZQgkyhEYpvuoyqj4ONz5xCO4ctINOLK3DK/e/xCOHqgUvEKCIHixlCHoShaTR+Armmpo0t2zcNVNk6C43Xj3uT/jn2+/a2iYPUEQwYs1DQHJR31GUw1dm3azNxm8/L9xuinwrUAIgjAPaxoCCg35zNEDlSj58G/Y/bfNKPv7Z6KXQxBEALCUIdDko6Qa8p321lasfXSp6GUQBBFALDWPgFRDBEEQfbGkIaDQEEEQRBeWMgQkHyUIguiLpQwBqYYIgiD6YjFDQL2GCIIgemMpQ0DzCAiCIPpiKUOgewSkGiIIgtCxmCEgj4AgCKI3ljIEpBoiCILoi6UMAdUREARB9MWahqCDcgQEQRAaljIEkky9hgiCIHpjKUMgOzo9AlINEQRB6FjKEFAdAUEQRF8sZQio+yhBEERfLGcI3B0dopdBEAQRVFjOEFDDOYIgiJ5YyhBIdpnyAwRBEL2wlCGQ7XbKDxAEQfTCUoZAsstUVUwQBNELSxkC2W4nQ0AQBNELLkMQGRmJoqIiVFRUoKioCBEREefdrqCgAC0tLfjggw96vJ+YmIht27ahsrISeXl5cDgcPMsZEDIEBEEQfeEyBEuWLMHmzZsxZswYbN68GUuWLDnvdn/84x9xzz339Hl/+fLleOGFF5CcnIyWlhbMnz+fZzkDItvt8LgpR0AQBNEdLkOQkZGB1atXAwBWr16NmTNnnne7LVu24MyZM33ev/nmm/HOO+8MuL+/kMgjIAiC6AOXIYiJiUFDQwMAoKGhATExMT7vGxUVhZMnT+p9f+rq6hAXF8eznAGRZZnqCAiCIHphH2iD4uJixMbG9nn/8ccf7/Oeqqr+WdV5yM7OxoIFCwAA0dHRTJ8hOUg+ShAE0ZsBDcG0adP6/V1jYyNiY2PR0NCA2NhYNDU1+Xzg5uZmREREeJ/SFQXx8fGor6/vd/vc3Fzk5uYCAFwul8/H6Q4liwmCIPrCFRrKz89HVlYWACArKwsbN240tP8nn3yCWbNmMe9vFDIEBEEQ50dl/bnooovUTZs2qRUVFWpxcbEaGRmpAlDHjRun5ubm6tv94x//UJuamtSzZ8+qtbW1alpamgpATUpKUrdv365WVlaq69atU51Op0/HdblcTOv9xZuvqve/+iLz/y/90A/90M9g/unv3jlgaOhCnDhxAlOnTu3zfklJCbKzs/XXN91003n3r6mpwcSJE3mWYAiqLCYIguiLtSqLZQoNEQRB9MZShsDbfZRUQwRBEN3hCg0NNiq+2IGTjb4rmwiCIKyApQxB/h//R/QSCIIggg5LhYYIgiCIvpAhIAiCsDhkCAiCICwOGQKCIAiLQ4aAIAjC4pAhIAiCsDhkCAiCICwOGQKCIAiLY4O3+9ygoqmpCYcPH2baNzo6GsePH/fzivihdRmD1mUMWpcxvqvrSkhIwKhRo877O+GtUc38YW1hTesKrh9aF62L1uW/HwoNEQRBWBwyBARBEBbHcobg1VdfFb2E80LrMgatyxi0LmNYbV2DMllMEARB+A/LeQQEQRBET8gQEARBWBzLGIL09HSUl5ejsrISixcvFraO+Ph4bNmyBV999RX27duHBx98EACQk5ODuro6lJaWorS0FDNmzBCyvpqaGnz55ZcoLS2Fy+UCAERGRqKoqAgVFRUoKipCRESEaesZM2aMfk5KS0tx6tQp/PKXvxR2vlauXInGxkbs3btXf+9C5+fFF19EZWUl9uzZg5SUFFPX9Yc//AH79+/Hnj178O6772LEiBEAvFrys2fP6ufu5ZdfNnVdF/rulixZgsrKSpSXlyMtLc3UdeXl5elrqqmpQWlpKQBzz1d/9wczrjHh2thA/0iSpFZVValJSUmqw+FQd+/erY4dO1bIWmJjY9WUlBQVgDp06FD1wIED6tixY9WcnBz117/+tfBzVVNTo0ZFRfV4b/ny5erixYtVAOrixYvVZcuWCfsejx07pl566aXCzteUKVPUlJQUde/evQOenxkzZqgff/yxCkCdOHGium3bNlPXNW3aNFWWZRWAumzZMn1dCQkJPbYz+3z1992NHTtW3b17t+p0OtXExES1qqpKlSTJtHV1//nTn/6kPvnkk6afr/7uD4G+xizhEaSmpqKqqgo1NTXo6OhAXl4eMjIyhKyloaFBf9L45ptvsH//fsTFxQlZi69kZGRg9erVAIDVq1dj5syZQtZxyy234ODBgzhy5IiQ4wPAp59+ihMnTvR4r7/zk5GRgTVr1gAAtm/fjoiICMTGxpq2ruLiYiiKAgDYtm0b4uPjA3Jso+vqj4yMDOTl5aG9vR2HDh1CVVUVUlNThaxrzpw5+Otf/xqQY1+I/u4Pgb7GLGEI4uLiUFtbq7+uq6sLiptvQkICUlJSsH37dgDAokWLsGfPHqxcudLU8Et3VFVFUVERdu7ciezsbABATEwMGhoaAHgv1JiYGCFry8zM7PHHGQznC+j//ATTdXffffehoKBAf52UlIRdu3Zh69atmDx5sunrOd93Fyzna8qUKWhsbERVVZX+nojz1f3+EOhrzBKGIBgZMmQINmzYgIceeghnzpzByy+/jMsvvxzXXXcdjh07hj//+c9C1jV58mSMGzcOM2bMwAMPPIApU6b02UZVVdPX5XA4cPvtt2P9+vUAEDTn63yIOD8X4rHHHoPb7cZbb70FADh27BguvfRSXH/99Xj44Yexdu1aDBs2zLT1BPN3BwB33313jwcOEeer9/2hN/6+xixhCOrr6zF69Gj9dXx8POrr64Wtx263Y8OGDXjrrbfw3nvvAfA20vN4PFBVFbm5uQFziQfi6NGjAICvv/4a7733HlJTU9HY2Ki7m7GxsWhqajJ9XTNmzMCuXbv0YwfL+QLQ7/kJhusuKysLt956K+bOnau/197erodFdu3ahYMHD2LMmDGmram/7y4Yzpcsy7jjjjvw9ttv6++Zfb7Od38I9DVmCUPgcrmQnJyMxMREOBwOZGZmIj8/X9h6Vq5cif379+OFF17Q3+se1/vxj3+Mffv2mb6u8PBwDB06VP93Wloa9u3bh/z8fGRlZQHw3lg2btxo+tp6P6UFw/nS6O/85OfnY968eQCAiRMn4tSpU7p7bwbp6en47W9/i9tvvx2tra36+9HR0ZAk759+UlISkpOTUV1dbdq6+vvu8vPzkZmZCafTicTERCQnJ2PHjh2mrQsApk6divLy8h43U7PP1/nuD2ZcY6Zkw0X/zJgxQz1w4IBaVVWlPvbYY8LWMWnSJFVVVXXPnj1qaWmpWlpaqs6YMUNds2aN+uWXX6p79uxRN27cqMbGxpq+tqSkJHX37t3q7t271X379unn6aKLLlI3bdqkVlRUqMXFxWpkZKSp6woPD1ePHz+uDh8+XH9P1Plau3atevToUbW9vV2tra1V77vvvguen5deekmtqqpSv/zyS3XcuHGmrquyslI9cuSIfp29/PLLKgD1jjvuUPft26eWlpaqJSUl6q233mrqui703T322GNqVVWVWl5erk6fPt3UdQFQV61apd5///09tjXzfPV3fwj0NUYtJgiCICyOJUJDBEEQRP+QISAIgrA4ZAgIgiAsDhkCgiAIi0OGgCAIwuKQISAIgrA4ZAgIgiAszv8HllHYSo4HMVsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fn(x):\n",
    "    match abs(int(x*10)):\n",
    "        case 0:\n",
    "            return .16\n",
    "        case 2:\n",
    "            return .13\n",
    "        case 5:\n",
    "            return .11\n",
    "        case 9:\n",
    "            return 1e-4\n",
    "        case _:\n",
    "            return x * (fn(x/2) if x < 100 else math.exp(x*x))\n",
    "\n",
    "pyl.plot([fn(x/100) for x in range(-100,101)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_fitness(population):\n",
    "    if type(population) == list:\n",
    "        return [(abs(fn(x)),x) for x in population]\n",
    "    else:\n",
    "        return abs(fn(population))\n",
    "\n",
    "def crossover_function(a, b):\n",
    "    rand_fun = random.random\n",
    "    rng = rand_fun()\n",
    "    if rng < .4888:\n",
    "        return (b-a)/2 + a*.1\n",
    "    elif rng < .88:\n",
    "        return (b-a)/2 + b*.1\n",
    "    else:\n",
    "        return (b-a)/2 + rand_fun()*.1\n",
    "\n",
    "def crossover(population, new_population_size: int):\n",
    "    rng = lambda: random.randint(0, len(population)-1)\n",
    "    choose = lambda: population[rng()]\n",
    "    xs = [crossover_function(choose(), choose()) for i in range(new_population_size)]\n",
    "    return xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best score:\n",
      "      converged: True\n",
      "           flag: 'converged'\n",
      " function_calls: 59\n",
      "     iterations: 58\n",
      "           root: -0.6000000000007168\n",
      "Lowest value @ root: -0.004320000000015484\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-0.00432, 0.0001)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_result: RootResults = root_scalar(fn, bracket=[-1.0, 1.0])\n",
    "print(f\"Best score:\\n{best_result}\\nLowest value @ root: {fn(best_result.root)}\")\n",
    "fn(-0.6000000000000000), fn(-0.9999914207085816)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.903 scored 0.0001 in 2 iterations\n"
     ]
    }
   ],
   "source": [
    "def run_ga(population_size = 1000, domain_size = 100, population_percent_keep = 0.1, iterations=1_000_0):\n",
    "    domain = [i/10 for i in range(-domain_size,domain_size+1)]\n",
    "    population = [domain[random.randint(0, len(domain)-1)] for _ in range(population_size)]\n",
    "\n",
    "    for its in range(1_000_0):\n",
    "        population_by_fitness = [y for _, y in sorted(calculate_fitness(population))]\n",
    "\n",
    "        best_score = calculate_fitness(population_by_fitness[0])\n",
    "        if best_score <= 1e-4:\n",
    "            print(f'{population_by_fitness[0]} scored {best_score} in {its} iterations')\n",
    "            break\n",
    "\n",
    "        next_generation = population_by_fitness[:int(population_size*population_percent_keep)]\n",
    "        top_half = population_by_fitness[:int(population_size*0.5)]\n",
    "\n",
    "        next_generation.extend(crossover(top_half, int(population_size*(1.0 - population_percent_keep))))\n",
    "\n",
    "        population = next_generation\n",
    "\n",
    "run_ga(population_size=5, iterations=1_000_000_000_000)"
   ]
  }
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