checking if 2 numbers of array add up to I

Question

I saw a interview question as follows: Give an unsorted array of integers A and and an integer I, find out if any two members of A add up to I.

any clues?

ti

Answer 1

If you have the range which the integers are within, you can use a counting sort-like solution where you scan over the array and count an array up. Ex you have the integers

input = [0,1,5,2,6,4,2]

And you create an array like this:

count = int[7]

which (in Java,C# etc.) are suited for counting integers between 0 and 6.

foreach integer in input
    count[i] = count[i] + 1

This will give you the array [1,1,2,0,1,1,1]. Now you can scan over this array (half of it) and check whether there are integers which adds up to i like

for j = 0 to count.length - 1
    if count[j] != 0 and count[i - j] != 0 then // Check for array out-of-bounds here
         WUHUU! the integers j and i - j adds up

Overall this algorithm gives you O(n + k) where n is from the scan over the input of length n and k is the scan over the count array of length k (integers between 0 and k - 1). This means that if n > k then you have a guaranteed O(n) solution.