{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "green-washer",
   "metadata": {},
   "outputs": [],
   "source": [
    "def insertion_sort(list_to_sort):\n",
    "    L = list(list_to_sort)\n",
    "    new_list = []\n",
    "  \n",
    "    while len(L) > 0:\n",
    "        # find the index of the smallest thing\n",
    "        min_index = min(range(len(L)), key=lambda i : L[i])\n",
    "        \n",
    "        # remove it from L and add it to new_list\n",
    "        new_list.append(L.pop(min_index))\n",
    "        \n",
    "    return new_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "photographic-punch",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "from time import time\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "sustainable-float",
   "metadata": {},
   "outputs": [],
   "source": [
    "L = [random.randint(1,1000000) for n in range(10000)] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "identified-awareness",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.3559629917144775\n"
     ]
    }
   ],
   "source": [
    "tt = time()\n",
    "R1 = insertion_sort(L)\n",
    "print(time()-tt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "forward-check",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00138092041015625\n"
     ]
    }
   ],
   "source": [
    "tt = time()\n",
    "R2 = sorted(L)\n",
    "print(time()-tt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "wired-vermont",
   "metadata": {},
   "outputs": [],
   "source": [
    "def merge_sort(L):\n",
    "    \n",
    "    # base case: a list of length 1 is already sorted\n",
    "    if len(L) <= 1:\n",
    "        return L\n",
    "    \n",
    "    # split the list (roughly) in hald\n",
    "    mid_point = math.ceil(len(L)/2)\n",
    "    left_half = L[:mid_point]\n",
    "    right_half = L[mid_point:]\n",
    "    \n",
    "    # recursively apply the function to the two halfs (divide)\n",
    "    LS = merge_sort(left_half)\n",
    "    RS = merge_sort(right_half)\n",
    "    \n",
    "    # time to conquer\n",
    "    full_list = []\n",
    "    \n",
    "    # while the two halves still have something left\n",
    "    while len(LS) + len(RS) > 0:\n",
    "        # either LS[0] or RS[0] is the smallest of all elements\n",
    "        # in LS and RS. Find it, remove it from its list, and\n",
    "        # add it to full_list\n",
    "        if LS:\n",
    "            if RS:\n",
    "                if LS[0] <= RS[0]:\n",
    "                    full_list.append(LS.pop(0))\n",
    "                else:\n",
    "                    full_list.append(RS.pop(0))\n",
    "            else:\n",
    "                full_list.append(LS.pop(0))\n",
    "        else:\n",
    "            full_list.append(RS.pop(0))\n",
    "    return full_list\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "accepting-diana",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.06351804733276367\n"
     ]
    }
   ],
   "source": [
    "tt = time()\n",
    "R3 = merge_sort(L)\n",
    "print(time()-tt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "typical-algeria",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R3 == R2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "automatic-season",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 0.000209808349609375\n",
      "100 0.00075531005859375\n",
      "\t3.6775320139697323\n",
      "1000 0.06404900550842285\n",
      "\t85.0360873694207\n",
      "10000 5.391217947006226\n",
      "\t84.17702854122228\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-12-5a7d85f24383>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mtt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mR\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minsertion_sort\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m     \u001b[0mtimes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mtt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-1-19bac1fad570>\u001b[0m in \u001b[0;36minsertion_sort\u001b[0;34m(list_to_sort)\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mwhile\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m         \u001b[0;31m# find the index of the smallest thing\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m         \u001b[0mmin_index\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m:\u001b[0m \u001b[0mL\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m         \u001b[0;31m# remove it from L and add it to new_list\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-1-19bac1fad570>\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(i)\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mwhile\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m         \u001b[0;31m# find the index of the smallest thing\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m         \u001b[0mmin_index\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m:\u001b[0m \u001b[0mL\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m         \u001b[0;31m# remove it from L and add it to new_list\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "times = []\n",
    "for p in range(1,6):\n",
    "    L = [random.randint(1,1000000) for n in range(10**p)] \n",
    "    \n",
    "    tt = time()\n",
    "    R = insertion_sort(L)\n",
    "    times.append(time()-tt)\n",
    "    \n",
    "    print(f\"{10**p} {time()-tt}\")\n",
    "    if len(times) > 1:\n",
    "        print(f\"\\t{times[-1]/times[-2]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "solar-shelf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 0.0023648738861083984\n",
      "100 0.0004220008850097656\n",
      "\t0.17847397675593735\n",
      "1000 0.005793094635009766\n",
      "\t13.746319365798415\n",
      "10000 0.07274603843688965\n",
      "\t12.568215521502719\n",
      "100000 1.458730936050415\n",
      "\t20.05314546419933\n"
     ]
    }
   ],
   "source": [
    "times = []\n",
    "for p in range(1,6):\n",
    "    L = [random.randint(1,1000000) for n in range(10**p)] \n",
    "    \n",
    "    tt = time()\n",
    "    R2 = merge_sort(L)\n",
    "    times.append(time()-tt)\n",
    "    \n",
    "    print(f\"{10**p} {time()-tt}\")\n",
    "    if len(times) > 1:\n",
    "        print(f\"\\t{times[-1]/times[-2]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "checked-announcement",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 9.799003601074219e-05\n",
      "100 1.5020370483398438e-05\n",
      "\t0.13819095477386933\n",
      "1000 0.0001399517059326172\n",
      "\t10.50909090909091\n",
      "10000 0.0017790794372558594\n",
      "\t12.865051903114187\n",
      "100000 0.017344951629638672\n",
      "\t9.780661646046262\n",
      "1000000 0.3232860565185547\n",
      "\t18.643429718544184\n",
      "10000000 4.332744836807251\n",
      "\t13.402582604552782\n"
     ]
    }
   ],
   "source": [
    "times = []\n",
    "for p in range(1,8):\n",
    "    L = [random.randint(1,1000000) for n in range(10**p)] \n",
    "    \n",
    "    tt = time()\n",
    "    R3 = sorted(L)\n",
    "    times.append(time()-tt)\n",
    "    \n",
    "    print(f\"{10**p} {time()-tt}\")\n",
    "    if len(times) > 1:\n",
    "        print(f\"\\t{times[-1]/times[-2]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "rough-breakdown",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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