{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "411ba309",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Improving Search\n",
    "\n",
    "#### CS 66: Introduction to Computer Science II"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c232cc8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## References for this lecture\n",
    "\n",
    "Problem Solving with Algorithms and Data Structures using Python\n",
    "\n",
    "Sections 6.1-6.5 [https://runestone.academy/ns/books/published/pythonds/SortSearch/toctree.html](https://runestone.academy/ns/books/published/pythonds/SortSearch/toctree.html)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9076d3ce",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Sequential Search\n",
    "\n",
    "As long as you can iterate through items in a data structure, you can write a _sequential search_ or _linear search_ - a search that runs in $O(n)$ time.\n",
    "\n",
    "We've been doing this all semester long: 1st week activity, _search_ in `OrderedList` class, etc.\n",
    "\n",
    "* for each item in the data structure\n",
    "    * check if the item is the one you're looking for"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09ab4f6d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "linear search of Python list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "93df93af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "15 in [3,5,2,4,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "33e476fb",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "def sequentialSearch(alist, item):\n",
    "    pos = 0\n",
    "    found = False\n",
    "    \n",
    "    while pos < len(alist) and not found:\n",
    "        if alist[pos] == item:\n",
    "            found = True\n",
    "        else:\n",
    "            pos = pos+1\n",
    "    return found\n",
    "\n",
    "testlist = [1, 2, 32, 8, 17, 19, 42, 13, 0]\n",
    "print(sequentialSearch(testlist, 3))\n",
    "print(sequentialSearch(testlist, 13))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b146ebd9",
   "metadata": {},
   "source": [
    "If the item is actually in the list\n",
    "* best case: 1 comparison\n",
    "* worst case: $n$ comparison\n",
    "* average case: $\\frac{n}{2}$ comparisons\n",
    "\n",
    "If the item is _not_ actually in the list\n",
    "* best case: $n$ comparison\n",
    "* worst case: $n$ comparison\n",
    "* average case: $n$ comparisons"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6be210c0",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Group Activity Problem 1\n",
    "\n",
    "If we knew that the list was in sorted order is it possible to make the sequential search end early? How?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "03ce85c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "testlist = [0, 1, 2, 8, 13, 17, 19, 32, 42]\n",
    "print(sequentialSearch(testlist, 3))\n",
    "print(sequentialSearch(testlist, 13))"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "4d2ede16",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Strategy for Guess-My-Number Game\n",
    "\n",
    "![clockgame.jpg](attachment:clockgame.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0413598e",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "Image credit: https://www.buzzerblog.com/2014/09/23/watch-the-price-is-right-revamps-clock-game/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0ce8a01",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Binary Search\n",
    "\n",
    "__Binary Search__ works by looking at the middle item within a given range and throwing out at least half the items on each iteration.\n",
    "\n",
    "_only works on a sorted data structure_\n",
    "\n",
    "Let's draw some pictures on the board to see how this works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "741feb7e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "def binarySearch(alist, item):\n",
    "    first = 0\n",
    "    last = len(alist)-1\n",
    "    found = False\n",
    "\n",
    "    while first<=last and not found:\n",
    "        midpoint = (first + last)//2\n",
    "        if alist[midpoint] == item:\n",
    "            found = True\n",
    "        else:\n",
    "            if item < alist[midpoint]:\n",
    "                last = midpoint-1\n",
    "            else:\n",
    "                first = midpoint+1\n",
    "\n",
    "    return found\n",
    "\n",
    "testlist = [0, 1, 2, 8, 13, 17, 19, 32, 42,]\n",
    "print(binarySearch(testlist, 3))\n",
    "print(binarySearch(testlist, 13))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8008bc48",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## Group Activity Problem 2:\n",
    "\n",
    "Write down how many items you have to look at _in the worst case_ for lists of the following size:\n",
    "* 100\n",
    "* 200\n",
    "* 400\n",
    "* 1000\n",
    "* 10000"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76cbe099",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Big-O analysis of Binary Search\n",
    "\n",
    "Things to notice\n",
    "* in each iteration, you can eliminate half the list\n",
    "* you can double the number of items in a list and only need to check one extra item\n",
    "* it does grow - so it isn't $O(1)$\n",
    "* it's much less than $O(n)$\n",
    "\n",
    "Binary Search is $O(\\log n)$ - inverse of exponential growth\n",
    "\n",
    "This is fantastic!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea37b1ed",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Ordered List Abstract Data Type\n",
    "\n",
    "The book implemented the Ordered List Abstract Data Type as a Linked List: [https://runestone.academy/ns/books/published/pythonds/BasicDS/ImplementinganOrderedList.html](https://runestone.academy/ns/books/published/pythonds/BasicDS/ImplementinganOrderedList.html)\n",
    "\n",
    "* Search was $O(n)$\n",
    "\n",
    "\n",
    "If we instead implement Ordered List as an Array (Python list)\n",
    "* Search is $O(\\log n)$\n",
    "* Both `add` and `remove` still $O(n)$ because items are shifted (but finding the spot is a *search*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc3263bf",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## O(1) search\n",
    "\n",
    "Sequential Search is $O(n)$\n",
    "\n",
    "Binary Search is $O(\\log n)$\n",
    "\n",
    "Is it possible to do search in $O(1)$ time?\n",
    "\n",
    "#### An Idea\n",
    "\n",
    "Let's say we have a collection of values to store like 1, 5, 6, 7, 9, 10, 13, 15, 18.\n",
    "\n",
    "We could represent this in a list like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ecdab7b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "my_collection = [None,1,None,None,None,5,6,7,None,9,10,None,None,13,None,15,None,None,18,None]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9487fbe3",
   "metadata": {},
   "source": [
    "Now, we can search if a value is in the collection by looking it up at its index. If it is not in the collection, `None` will be returned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1c123093",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "18\n",
      "None\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "print( my_collection[5] )\n",
    "print( my_collection[18] )\n",
    "print( my_collection[4] )\n",
    "print( my_collection[17] )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b323bbbd",
   "metadata": {},
   "source": [
    "## Group Activity Problem 3:\n",
    "\n",
    "Because list access is $O(1)$, this does search in $O(1)$. So, are the downsides to this approach?\n",
    "\n",
    "\n",
    "Could we make an `UnorderedList` this way? How about an `OrderedList`? How about a `Set`?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9215744a",
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   "source": [
    "## Hash Tables\n",
    "\n",
    "Hash tables work like the above approach, except it allows for values outside of indices of the table using a __hash function__.\n",
    "\n",
    "Hash functions can be any function that transforms a value into a suitable index for the list. \n",
    "\n",
    "For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7c6d220d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[None, None, None, None, None, None, None, None, None, None]\n"
     ]
    }
   ],
   "source": [
    "hash_table_size = 10\n",
    "hash_table = [None] * 10 #initialize all 10 spots to None\n",
    "\n",
    "def simple_hash(value,num_items):\n",
    "    return value % num_items\n",
    "\n",
    "print(hash_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "608ca51d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now let's put a value into the hash table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d947b485",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[None, None, None, None, None, None, None, 87, None, None]\n"
     ]
    }
   ],
   "source": [
    "val = 87\n",
    "val_hash = simple_hash(val,hash_table_size)\n",
    "hash_table[val_hash] = val\n",
    "print(hash_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c01087d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Doing a few more:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "02485328",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[None, None, 112, 33, None, None, None, 87, None, 19]\n"
     ]
    }
   ],
   "source": [
    "hash_table[simple_hash(33,hash_table_size)] = 33\n",
    "hash_table[simple_hash(112,hash_table_size)] = 112\n",
    "hash_table[simple_hash(19,hash_table_size)] = 19\n",
    "print(hash_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "787d0a25",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now we can search the hash table like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "08e7bdc6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_table[simple_hash(33,hash_table_size)] == 33 #is 33 at the spot is should be in the hash table?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8b4d8658",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_table[simple_hash(12,hash_table_size)] == 12 #is 12 at the spot is should be in the hash table?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a808ca97",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## Group Activity Problem 4\n",
    "\n",
    "There's still a problem with this approach. What is it?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dbdd095",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "## Collisions\n",
    "\n",
    "When two different items end up with the same hash value, it is called a __collision__.\n",
    "\n",
    "This is a problem since both items can't occupy the same memory location.\n",
    "\n",
    "__Collision Resolution__ is the process of finding a new location for an item when there is a collision - we'll talk about some approaches next time.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca1af1bd",
   "metadata": {},
   "source": [
    "## Hash functions for strings\n",
    "\n",
    "If you want to put strings in your hash table, you have to come up with a way to convert them into numbers. \n",
    "\n",
    "One approach is to use the `ord` function for each character, which returns the unicode value used to represent the character in memory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "41ad7cdb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ord('c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c0daa81a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "97"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ord('a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7fb29075",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "116"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ord('t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "590228d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "4\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "def string_hash(astring, tablesize):\n",
    "    sum = 0\n",
    "    for pos in range(len(astring)):\n",
    "        sum = sum + ord(astring[pos])\n",
    "\n",
    "    return sum%tablesize\n",
    "\n",
    "print( string_hash(\"cat\",10) )\n",
    "print( string_hash(\"dog\",10) )\n",
    "print( string_hash(\"chicken\",10) )"
   ]
  }
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