day 19 - counting inversions.ipynb

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   "source": [
    "import numpy as np"
   ]
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   "source": [
    "## algorithm"
   ]
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    "def inversions(items):\n",
    "    n = len(items)\n",
    "    if n <= 1:\n",
    "        return items, 0\n",
    "\n",
    "    # number of inversions in partitions\n",
    "    left, linv = inversions(items[:n // 2])\n",
    "    right, rinv = inversions(items[n // 2:])\n",
    "\n",
    "    inv = linv + rinv\n",
    "    llen, rlen = len(left), len(right)\n",
    "    i, j, aux = 0, 0, []\n",
    "\n",
    "    # merge and count inversions\n",
    "    for k in range(n):\n",
    "        if i < llen and j < rlen and left[i] > right[j]:\n",
    "            inv += llen - i\n",
    "            aux.append(right[j])\n",
    "            j += 1\n",
    "        elif i < llen:\n",
    "            aux.append(left[i])\n",
    "            i += 1\n",
    "        else:\n",
    "            aux.append(right[j])\n",
    "            j += 1\n",
    "    \n",
    "    return aux, inv"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## run"
   ]
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   "execution_count": 3,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "[29, 25, 17, 15, 6, 8, 11, 15, 7, 5]"
      ]
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     "execution_count": 3,
     "metadata": {},
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   "source": [
    "items = list(np.random.randint(0, 30, 10))\n",
    "items"
   ]
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   "execution_count": 4,
   "metadata": {
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    {
     "data": {
      "text/plain": [
       "([5, 6, 7, 8, 11, 15, 15, 17, 25, 29], 37)"
      ]
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "inversions(items)"
   ]
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   "execution_count": null,
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    "collapsed": true
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   "source": []
  }
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