The missing number problem

A list contains all the ints between 1 and n, but one of them is missing. (The list is of length n-1). What is the missing integer?

Here is one possible solution:

def missing_k(L):
    n = len(L) + 1
    #Try every k: 1, 2, 3, ..., n, and see which
    #k is missing
    for k in range(1, n+1):
        if k not in L:
            return k
    #will never get here, since one of the k's will 
    #not be in L and we'll return it

Let's rewrite this a little bit, imagining that we can't use k not in L

def elem_in_list(elem, L):
    '''Return True iff elem is in L'''
    for e in L:
        if e == elem:
            return True
    
    #Tried every element, and didn't find any of them
    #in L
    return False

def missing_k(L):
    n = len(L) + 1
    for k in range(1, n+1):
        if not elem_in_list(k, L):
            return k

Note that we have to look through the list many times (n times, in fact -- we potentially look through the entire list every time we call elem_in_list) in order to solve the problem this way