Contents

Searching

Search Problem Definition

Given a list aList of length n and an item, is item present in aList?

• If item is in aList, return True

• else return False

Searching in an Unsorted List

Let’s start with a unsorted list first.

def linearSearch(aList, item):
    n = len(aList)
    for el in aList:
        if item == el:
            return True
    return False

linearSearch([12, 16, 23, 2, 7], 16)

True

linearSearch([12, 16, 23, 2, 7], 13)

False

linearSearch(['a', 'e', 'i', 'o', 'u'], 'u')

True

linearSearch(['a', 'e', 'i', 'o', 'u'], 'a')

True

linearSearch(['hello', 'world', 'silly'], 'hi')

False

Searching in a Sorted List

Can we do better if the given list aList is sorted? Yes!

Let’s implement a binary search function below.

def binarySearch(aList, item):
    """Assume aList is sorted. If item is 
    in aList, return True; else return False."""
    n = len(aList)
    mid = n // 2
    # base case 1
    if n == 0:
        return False
    
    # base case 2
    elif item == aList[mid]:
        return True
    
    # recurse on left
    elif item < aList[mid]:
        return binarySearch(aList[:mid], item)
        
    # recurse on right
    else:
        return binarySearch(aList[mid + 1:], item)

binarySearch(['a', 'e', 'i', 'o', 'u'], 'a')

True

binarySearch(['a', 'e', 'i', 'o', 'u'], 'b')

False

binarySearch(sorted(['hello', 'world', 'silly']), 'hi')

False

binarySearch(sorted(['hello', 'world', 'silly']), 'hello')

True

numList = [23, 1, 2, 90, 0, 10, 12, 120, 45]
numList.sort()

numList

[0, 1, 2, 10, 12, 23, 45, 90, 120]

binarySearch(numList, 11)

False

binarySearch(numList, 45)

True