{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "def changeDp(money, coins):\n",
    "    D = numpy.zeros((len(coins), (money + 1)), dtype = int)\n",
    "    # Initialize first row of the matrix\n",
    "    D[0,1:] = range(1, money + 1)\n",
    "    for i in range(1, len(coins)):\n",
    "        for j in range(0, money + 1):\n",
    "            if j < coins[i]:\n",
    "                D[i,j] = D[i-1,j]\n",
    "            else:\n",
    "                D[i,j] = min(D[i-1,j],\n",
    "                            D[i,j - coins[i]] + 1)\n",
    "    return D[-1][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "changeDp(12, [1,4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coins = [50,25,20,10,5,1][::-1]\n",
    "changeDp(40, coins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "735"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coins = [1,3,5,11,20,21,22]\n",
    "changeDp(16164, coins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "def changeDp(money, coins):\n",
    "    D = numpy.zeros((len(coins), (money + 1)), dtype = int)\n",
    "    # Initialize first row of the matrix\n",
    "    D[0,1:] = range(1, money + 1)\n",
    "    for i in range(1, len(coins)):\n",
    "        for j in range(0, money + 1):\n",
    "            if j < coins[i]:\n",
    "                D[i,j] = D[i-1,j]\n",
    "            else:\n",
    "                D[i,j] = min(D[i-1,j],\n",
    "                            D[i,j - coins[i]] + 1)\n",
    "    return D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "        17, 18, 19, 20],\n",
       "       [ 0,  1,  2,  1,  2,  3,  2,  3,  4,  3,  4,  5,  4,  5,  6,  5,  6,\n",
       "         7,  6,  7,  8]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "changeDp(20, [2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def DPChange(money,coins):\n",
    "    MinNumCoins = {}\n",
    "    MinNumCoins[0] = 0\n",
    "    for m in range(1,money+1):\n",
    "        MinNumCoins[m] = float('inf')\n",
    "        for i in range(len(coins)):\n",
    "            if m >= coins[i]:\n",
    "                if MinNumCoins[m-coins[i]] + 1 < MinNumCoins[m]:\n",
    "                               MinNumCoins[m] = MinNumCoins[m-coins[i]] + 1\n",
    "    return MinNumCoins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0,\n",
       " 1: inf,\n",
       " 2: 1,\n",
       " 3: 1,\n",
       " 4: 2,\n",
       " 5: 2,\n",
       " 6: 2,\n",
       " 7: 3,\n",
       " 8: 3,\n",
       " 9: 3,\n",
       " 10: 4,\n",
       " 11: 4,\n",
       " 12: 4,\n",
       " 13: 5,\n",
       " 14: 5,\n",
       " 15: 5,\n",
       " 16: 6,\n",
       " 17: 6,\n",
       " 18: 6,\n",
       " 19: 7,\n",
       " 20: 7,\n",
       " 21: 7,\n",
       " 22: 8,\n",
       " 23: 8,\n",
       " 24: 8}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DPChange(20, [2,3])"
   ]
  }
 ],
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  "kernelspec": {
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  "language_info": {
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