3 sum and 2 sum problem

Q: Given an integer x and an unsorted array of integers, describe an algorithm to determine whether two of the numbers add up to x.

If we have hash table, we can just check for every number ‘a’, if x-‘b’ is present in hash table. This takes O( n ) with constant space for hashtable. What if the interviewer hates the hashtable.

Sort the array. Then, keep track of two pointers in the array, one at the beginning and one at the end. Whenever the sum of the current two integers is less than x, move the first pointer forwards, and whenever the sum is greater than x, move the second pointer backwards. This solution takes O(n log n) time because we sort the numbers.

Another approach for this problem could be…

Create a binary search tree containing x minus each element in the array. Then, check whether any element of the array appears in the BST. It takes O(n log n) time to create a binary search tree from an array, since it takes O(log n) time to insert something into a BST, and it takes O(n log n) time to see if any element in an array is in a BST, since the lookup time for each element in the array takes O(log n). Therefore step one takes O(n log n) time and step two takes O(n log n) time, so our total running time is O(n log n).

Variations for this problem would be, find three integers a,b,c in the array such that a+b=c

This will  take O(n²) time complexity.

Other variation is Find three integers a,b,c in the array such that a+b+c =0