day 35 - median.ipynb

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   "source": [
    "import numpy as np"
   ]
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   "source": [
    "## algorithm"
   ]
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   "source": [
    "def kth(items, k, depth=1):\n",
    "    if len(items) == 1:\n",
    "        return items[0], depth\n",
    "\n",
    "    # randomize on pivot\n",
    "    pivot = np.random.choice(items)\n",
    "    split = np.sum(items <= pivot)\n",
    "    \n",
    "    # search partition\n",
    "    if k < split:\n",
    "        return kth(items[items <= pivot], k, depth + 1)\n",
    "    else:\n",
    "        return kth(items[items > pivot], k - split, depth + 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## run"
   ]
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [],
   "source": [
    "items = np.arange(1000000)\n",
    "np.random.shuffle(items)"
   ]
  },
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   "execution_count": 4,
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     "data": {
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       "(500000, 29)"
      ]
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "kth(items, len(items) // 2)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
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    {
     "data": {
      "text/plain": [
       "(0, 14)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "kth(items, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(999999, 16)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kth(items, len(items) - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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