euler-002-even-fibonacci-numbers-20130607.ipynb

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   "source": [
    "[Even Fibonacci numbers](https://projecteuler.net/problem=2)\n",
    "\n",
    "[Problem](https://projecteuler.net/archives) 2\n",
    "\n",
    "Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:\n",
    "\n",
    "    1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...\n",
    "\n",
    "By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "n = 4000000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def foo(n):\n",
    "    a = 0\n",
    "    b = 1\n",
    "    total = 0\n",
    "    while True:\n",
    "        c = a + b\n",
    "        a = b\n",
    "        b = c\n",
    "        # print b\n",
    "        if b > n:\n",
    "            break\n",
    "        if b % 2 == 0:\n",
    "            total += b\n",
    "    return total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 9.17 µs per loop\n"
     ]
    },
    {
     "data": {
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       "4613732"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%timeit foo(n)\n",
    "correct_answer = foo(n)\n",
    "correct_answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fib(last):\n",
    "    a = 0\n",
    "    b = 1\n",
    "    while True:\n",
    "        c = a + b\n",
    "        a = b\n",
    "        b = c\n",
    "        if b > last:\n",
    "            break\n",
    "        yield b\n",
    "\n",
    "def foo(n):\n",
    "    return sum([f for f in fib(n) if f % 2 == 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 13.2 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit foo(n)\n",
    "assert foo(n) == correct_answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def even_fibonacci(last):\n",
    "    a = 0\n",
    "    b = 1\n",
    "    while True:\n",
    "        c = a + b\n",
    "        a = b\n",
    "        b = c\n",
    "        if b > last:\n",
    "            break\n",
    "        if b % 2 == 0:\n",
    "            yield b\n",
    "\n",
    "def foo(n):\n",
    "    return sum([f for f in even_fibonacci(n)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 11.9 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit foo(n)\n",
    "assert foo(n) == correct_answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def unrolled_even_fibonacci(last):\n",
    "    a = 0\n",
    "    b = 1\n",
    "    while True:\n",
    "        c = a + b\n",
    "        a = b\n",
    "        b = c\n",
    "        c = a + b\n",
    "        a = b\n",
    "        b = c\n",
    "        if b > last:\n",
    "            break\n",
    "        yield b\n",
    "        c = a + b\n",
    "        a = b\n",
    "        b = c\n",
    "\n",
    "def foo(n):\n",
    "    return sum([f for f in unrolled_even_fibonacci(n)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 7.44 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit foo(n)\n",
    "assert foo(n) == correct_answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def unrolled_even_fibonacci(last):\n",
    "    a = 0\n",
    "    b = 1\n",
    "    while True:\n",
    "        c = a + b\n",
    "        d = b + c\n",
    "        if d > last:\n",
    "            break\n",
    "        yield d\n",
    "        e = c + d\n",
    "        a = d\n",
    "        b = e\n",
    "\n",
    "def foo(n):\n",
    "    return sum([f for f in unrolled_even_fibonacci(n)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 6.37 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit foo(n)\n",
    "assert foo(n) == correct_answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def unrolled_even_fibonacci(last):\n",
    "    '''\n",
    "    The body of the loop reminds me of a musical round.\n",
    "    I like how there are no wasted assignments.\n",
    "    '''\n",
    "    a = 0\n",
    "    b = 1\n",
    "    while True:\n",
    "        c = a + b  # Frère Jacques, frère Jacques,\n",
    "        a = b + c  # Dormez-vous? Dormez-vous?\n",
    "        if a > last:\n",
    "            break\n",
    "        yield a\n",
    "        b = c + a  # Sonnez les matines! Sonnez les matines!\n",
    "\n",
    "def foo(n):\n",
    "    return sum([f for f in unrolled_even_fibonacci(n)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 5.8 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit foo(n)\n",
    "assert foo(n) == correct_answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def unrolled_even_fibonacci(last):\n",
    "    '''\n",
    "    The body of the loop reminds me of a musical round.\n",
    "    I like how there are no wasted assignments.\n",
    "    '''\n",
    "    a = 0\n",
    "    b = 1\n",
    "    while True:\n",
    "        c = a + b  # Frère Jacques, frère Jacques,\n",
    "        a = b + c  # Dormez-vous? Dormez-vous?\n",
    "        if a > last:\n",
    "            break\n",
    "        yield a\n",
    "        b = c + a  # Sonnez les matines! Sonnez les matines!\n",
    "\n",
    "def foo(n):\n",
    "    return sum(unrolled_even_fibonacci(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 4.24 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit foo(n)\n",
    "assert foo(n) == correct_answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sum_even_fibonacci(last):\n",
    "    '''\n",
    "    The body of the loop reminds me of a musical round.\n",
    "    I like how there are no wasted assignments.\n",
    "    '''\n",
    "    total = 0\n",
    "    a = 0\n",
    "    b = 1\n",
    "    while True:\n",
    "        c = a + b\n",
    "        a = b + c\n",
    "        if a > last:\n",
    "            return total\n",
    "        total += a\n",
    "        b = c + a\n",
    "\n",
    "def foo(n):\n",
    "    return sum_even_fibonacci(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 3.92 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit foo(n)\n",
    "assert foo(n) == correct_answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sum_even_fibonacci(last):\n",
    "    '''\n",
    "    The body of the loop reminds me of a musical round.\n",
    "    I like how there are no wasted assignments.\n",
    "\n",
    "    Aligned test with beginning of loop, hoping for small speed increase,\n",
    "    albeit at cost of ugly duplicated code before loop.\n",
    "    Loop code itself got easier to read.'''\n",
    "\n",
    "    total = 0\n",
    "    a = 0\n",
    "    b = 1\n",
    "    c = a + b\n",
    "    a = b + c\n",
    "    while a <= last:\n",
    "        total += a\n",
    "        b = c + a\n",
    "        c = a + b\n",
    "        a = b + c\n",
    "    return total\n",
    "\n",
    "def foo(n):\n",
    "    return sum_even_fibonacci(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 3.9 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit foo(n)\n",
    "assert foo(n) == correct_answer"
   ]
  }
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