hill_climbing.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "hill_climbing.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Erickrus/leetcode/blob/master/hill_climbing.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "metadata": {
        "id": "mSzomZJJRu8a",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 337
        },
        "outputId": "96c32bbb-03f9-4076-e3aa-2113b1f8f8d6"
      },
      "cell_type": "code",
      "source": [
        "# Discrete Space Hill Climbing Algorithm\n",
        "# https://en.wikipedia.org/wiki/Hill_climbing\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline \n",
        "\n",
        "def hill_climb(area, startNode):\n",
        "  i = 0\n",
        "  currNode = startNode\n",
        "  # loop do\n",
        "  while True:\n",
        "    # L = NEIGHBORS(currentNode);\n",
        "    neighborList = neighbors(area, currNode)\n",
        "    nextVal, nextNode = -9999, -1\n",
        "    for node in neighborList:\n",
        "      if area[node] > nextVal:\n",
        "        nextNode = node\n",
        "        nextVal = area[node]\n",
        "    if nextVal <= area[currNode]:\n",
        "      # Return current node since no better neighbors exist\n",
        "      return currNode\n",
        "    currNode = nextNode\n",
        "    \n",
        "    # unable to converge, just quit\n",
        "    # this is additional\n",
        "    i += 1\n",
        "    if i > len(area) * 5:\n",
        "      print(\"exiting\")\n",
        "      return currNode\n",
        "\n",
        "def neighbors(area, currNode):\n",
        "  size,res = 3, []\n",
        "  # left pass\n",
        "  i = 1\n",
        "  while i <= size and currNode-i>0:\n",
        "    res.append(currNode-i)\n",
        "    i += 1\n",
        "  # right pass\n",
        "  i = 1\n",
        "  while i <= size and currNode+i<len(area)-1:\n",
        "    res.append(currNode+i)\n",
        "    i += 1\n",
        "  return res\n",
        "area = [1,2,3,5,4,6,7,11,5,6,6,6,6,6,10,12,12,5,2,2,2,0]\n",
        "plt.fill_between( range(len(area)),area, color=\"skyblue\", alpha=0.9)\n",
        "plt.plot(range(len(area)),area)\n",
        "\n",
        "# approaching from the start\n",
        "node = hill_climb(area,0)\n",
        "print(\"area[%d] => area[%d] = %d\"%(0, node, area[node]))\n",
        "print(\"reached local maxima\")\n",
        "\n",
        "# approaching from the end\n",
        "node = hill_climb(area,len(area)-4)\n",
        "print(\"area[%d] => area[%d] = %d\"%(len(area)-4, node, area[node]))\n",
        "print(\"reached global maxima\")\n"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "area[0] => area[7] = 11\n",
            "reached local maxima\n",
            "area[18] => area[16] = 12\n",
            "reached global maxima\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAD4CAYAAAAjKGdbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neQshRB2S5C2EEHXo/wNG1uk7BvPkegAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fc659264710>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}