{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 사다리 게임 확률 분석\n",
    "사다리 게임은 한국과 일본에서만 주로 하는 것으로 보이며, 영미권에서는 관련 자료를 거의 찾아볼 수 없다.  \n",
    "오픈소스 구현을 발견하지 못해 직접 간단한 사다리 알고리즘을 구현해서 확률을 관찰 해보도록 한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "length = 12 # 사다리의 길이\n",
    "width = 8 # 사다리의 너비(선택가능한 갯수)\n",
    "\n",
    "ladder = None # 사다리 배열\n",
    "pos = None # 진행 경과를 저장하기 위한 임시 배열"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 가로 발판 위치를 랜덤하게 뽑아준다.\n",
    "def get_step(ladder, pos):\n",
    "    width = int((ladder.shape[1] + 1) / 2)\n",
    "    randomized_step = random.randint(1, width - 1) * 2 - 1\n",
    "\n",
    "    if (randomized_step - 2 >= 1 and ladder[pos, randomized_step - 2] == 1) or \\\n",
    "            (randomized_step + 2 <= width * 2 - 3 and ladder[pos, randomized_step + 2] == 1):\n",
    "        return get_step(ladder, pos)\n",
    "    else:\n",
    "        return randomized_step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "# 길이, 너비 만큼의 사다리를 생성한다.\n",
    "def make_ladder(length=10, width=10):\n",
    "    global ladder\n",
    "    ladder = np.zeros((length, width * 2 - 1), dtype=int)\n",
    "    global pos\n",
    "    pos = np.zeros(length, dtype=int)\n",
    "\n",
    "    # 가로 발판을 생성한다.\n",
    "    for i in range(1, length - 1):\n",
    "        ladder[i, get_step(ladder, i)] = 1\n",
    "#         ladder[i, get_step(ladder, i)] = 1\n",
    "#         ladder[i, get_step(ladder, i)] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def play_ladder(ladder, pos, start_point=1):\n",
    "    pos[0] = (start_point - 1) * 2 # 출발지\n",
    "    length = ladder.shape[0]\n",
    "    width = int((ladder.shape[1] + 1) / 2)\n",
    "    \n",
    "    for j in range(1, length):\n",
    "        prev_pos = pos[j - 1]\n",
    "            \n",
    "        if prev_pos > 1 and ladder[j, prev_pos - 1] == 1:\n",
    "            pos[j] = prev_pos - 2\n",
    "        elif prev_pos < (width - 1) * 2 and ladder[j, prev_pos + 1] == 1:\n",
    "            pos[j] = prev_pos + 2\n",
    "        else:\n",
    "            pos[j] = prev_pos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],\n",
       "       [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "make_ladder(length, width)\n",
    "play_ladder(ladder, pos, 1)\n",
    "\n",
    "# 사다리 형태 점검\n",
    "np.set_printoptions(threshold=np.nan)\n",
    "ladder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 1, 2, 2, 2, 3, 1, 2, 1])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 사다리를 count 만큼 시도한다.\n",
    "def try_ladder(count=100, start_point=1):\n",
    "    X = np.full(count, start_point)\n",
    "    y = []\n",
    "\n",
    "    for x in np.nditer(X):\n",
    "        if start_point == 0: # 시작점을 0으로 지정할 경우 랜덤하게 시작한다.\n",
    "            x = np.random.randint(width) + 1\n",
    "        make_ladder(length, width)\n",
    "        play_ladder(ladder, pos, x)\n",
    "\n",
    "        y.append(int(pos[-1] / 2 + 1))\n",
    "    \n",
    "    return np.array(y)\n",
    "\n",
    "y = try_ladder(10, 1)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# matplotlib의 hist() 그리드가 직관적이지 않아 bar()로 표현하도록 한다.\n",
    "# bar()를 그리기 위해 누적을 직접 계산해 histogram을 만든다.\n",
    "def make_hist(y):\n",
    "    z = np.zeros(width, dtype=int)\n",
    "    \n",
    "    for x in np.nditer(y):\n",
    "        z[x - 1] += 1\n",
    "        \n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112aae358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 ~ 10 까지 각 출발점에 따른 도착점 분포를 2x5 plot에 표현한다.\n",
    "fig, axs = plt.subplots(2, 5, figsize=(20, 10))\n",
    "\n",
    "start_point = 1\n",
    "for i in range(2):\n",
    "    for j in range(5):\n",
    "        if start_point > width:\n",
    "            break\n",
    "        y = try_ladder(100000, start_point)\n",
    "        \n",
    "        axs[i, j].set_title(start_point)\n",
    "        axs[i, j].bar(np.arange(1, width + 1), make_hist(y))\n",
    "        \n",
    "        start_point += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1032d7b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 출발점이 랜덤인 경우 도착점 분포\n",
    "plt.xticks(np.arange(1, width + 1))\n",
    "\n",
    "y = try_ladder(10000, 0)  # 시작점을 랜덤하게 정한다.\n",
    "plt.bar(np.arange(1, width + 1), make_hist(y))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x107db07f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 『통계의 힘』 책에서 나온대로 동일하게 실험한다.\n",
    "def try_ladder_as_book(count=100, start_point=0, end_point=1):\n",
    "    X = np.full(count, start_point)\n",
    "    y = []\n",
    "\n",
    "    for x in np.nditer(X):\n",
    "        if start_point == 0: # 시작점을 0으로 지정할 경우 랜덤하게 시작한다.\n",
    "            x = np.random.randint(width) + 1\n",
    "        make_ladder(length, width)\n",
    "        play_ladder(ladder, pos, x)\n",
    "\n",
    "        if int(pos[-1] / 2 + 1) == end_point:\n",
    "            y.append(x)\n",
    "    \n",
    "    return np.array(y)\n",
    "\n",
    "# --\n",
    "plt.xticks(np.arange(1, width + 1))\n",
    "\n",
    "length = 12\n",
    "y = try_ladder_as_book(8000, 0, 4)\n",
    "plt.bar(np.arange(1, width + 1), make_hist(y))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8Z6Y3+WrOl6vLTrfw/OhHP9IvfvELSZLD4ZC/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\n//79u7zNry88A2pkbG+L21OueJ6yt7kqZxpMAAC4HkNvPSeukbHJ2TV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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10795dfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 계단 갯수(length)에 따른 도착점 분포를 표현한다.\n",
    "fig, axs = plt.subplots(2, 5, figsize=(20, 10))\n",
    "\n",
    "length = 10\n",
    "for i in range(2):\n",
    "    for j in range(5):\n",
    "        y = try_ladder(10000, 1)\n",
    "        \n",
    "        axs[i, j].set_title(length)\n",
    "        axs[i, j].bar(np.arange(1, width + 1), make_hist(y))\n",
    "        \n",
    "        length += 10"
   ]
  }
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