{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.\n",
    "\n",
    "Find the sum of all the multiples of 3 or 5 below 1000.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "232169\n"
     ]
    }
   ],
   "source": [
    "# Classic off-by-one error.\n",
    "# https://en.wikipedia.org/wiki/Off-by-one_error\n",
    "total = 0\n",
    "euler = 0\n",
    "while euler < 999:\n",
    "    if (euler % 3 == 0) | (euler % 5 == 0):\n",
    "        total = total + euler\n",
    "    euler = euler + 1\n",
    "    \n",
    "print(total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "233168\n"
     ]
    }
   ],
   "source": [
    "# Fix off-by-one error by changing comparison operator\n",
    "total = 0\n",
    "euler = 0\n",
    "while euler <= 999:\n",
    "    if (euler % 3 == 0) | (euler % 5 == 0):\n",
    "        total = total + euler\n",
    "    euler = euler + 1\n",
    "\n",
    "print(total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "233168\n"
     ]
    }
   ],
   "source": [
    "# Replace magic number with a variable (n).\n",
    "# Also, let the machine do the dirty work.\n",
    "# That's why n is 1000 and the comparision is with n - 1.\n",
    "# Having the computer calculate n - 1 is the dirty work.\n",
    "\n",
    "n = 1000\n",
    "    \n",
    "total = 0\n",
    "euler = 0\n",
    "while euler <= n - 1:\n",
    "    if (euler % 3 == 0) | (euler % 5 == 0):\n",
    "        total = total + euler\n",
    "    euler = euler + 1\n",
    "    \n",
    "print(total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "233168\n"
     ]
    }
   ],
   "source": [
    "# Use n instead of n-1 for standard programming conventions.  \n",
    "# For loops that execute n times and start at 0\n",
    "# the convention is to initialize the loop counter with 0\n",
    "# for the comparision to be loop counter less than n.\n",
    "#\n",
    "# The C version of the idiom is\n",
    "#\n",
    "#     for (euler = 0; euler < n; euler++)\n",
    "#         ; /* whatever */\n",
    "    \n",
    "n = 1000\n",
    "    \n",
    "total = 0\n",
    "euler = 0\n",
    "while euler < n:\n",
    "    if (euler % 3 == 0) | (euler % 5 == 0):\n",
    "        total = total + euler\n",
    "    euler = euler + 1\n",
    "        \n",
    "print(total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "233168\n"
     ]
    }
   ],
   "source": [
    "# Replace the increment with variable name += increment.\n",
    "    \n",
    "n = 1000\n",
    "    \n",
    "total = 0\n",
    "euler = 0\n",
    "while euler < n:\n",
    "    if (euler % 3 == 0) | (euler % 5 == 0):\n",
    "        total = total + euler\n",
    "    euler += 1\n",
    "        \n",
    "print(total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "233168\n"
     ]
    }
   ],
   "source": [
    "# Don't stop at one bug.\n",
    "# Replace the increment with variable name += increment.\n",
    "# This time with accumulating the total.\n",
    "    \n",
    "n = 1000\n",
    "    \n",
    "total = 0\n",
    "euler = 0\n",
    "while euler < n:\n",
    "    if (euler % 3 == 0) | (euler % 5 == 0):\n",
    "        total += euler\n",
    "    euler += 1\n",
    "        \n",
    "print(total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "233168\n"
     ]
    }
   ],
   "source": [
    "# Replace | with or for readability.\n",
    "# It's more than readability, it's the wrong operator.\n",
    "# This is a bitwise or (0 or 1).  It will always program both sides of the equation.\n",
    "# 'or' compares to False.  This is safer if I could get per say a div/0.\n",
    "    \n",
    "n = 1000\n",
    "    \n",
    "total = 0\n",
    "euler = 0\n",
    "while euler < n:\n",
    "    if (euler % 3 == 0) or (euler % 5 == 0):\n",
    "        total += euler\n",
    "    euler += 1\n",
    "        \n",
    "print(total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def foo(total):\n",
    "    #total = 0\n",
    "    for euler in range(1000):\n",
    "        if (euler % 3 == 0) | (euler % 5 == 0):\n",
    "            total = total + euler\n",
    "    \n",
    "    #print(total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 281 µs per loop\n"
     ]
    }
   ],
   "source": [
    "import timeit\n",
    "%timeit foo(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "233168\n"
     ]
    }
   ],
   "source": [
    "total = 0\n",
    "\n",
    "for euler in range(1000):\n",
    "    if (euler % 3 == 0) | (euler % 5 == 0):\n",
    "        total = total + euler\n",
    "    \n",
    "print(total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def foo(n):\n",
    "    total = 0\n",
    "\n",
    "    for euler in range(n):\n",
    "        if (euler % 3 == 0) or (euler % 5 == 0):\n",
    "            total = total + euler\n",
    "\n",
    "    return total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 10\n",
    "foo(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 208 µs per loop\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "233168"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 1000\n",
    "%timeit foo(n)\n",
    "foo(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def foo(n):\n",
    "    total = 0\n",
    "\n",
    "    for i in range(n):\n",
    "        if (i % 3 == 0) or (i % 5 == 0):\n",
    "            total += i\n",
    "\n",
    "    return total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 209 µs per loop\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "233168"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 1000\n",
    "%timeit foo(n)\n",
    "foo(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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