3Sum

Problem

Given an array S of n integers, are there elements a, b, c in S such that a + b + c = 0? Find all unique triplets in the array which gives the sum of zero.

Example

For example, given array S = {-1 0 1 2 -1 -4}, A solution set is:

(-1, 0, 1)
(-1, -1, 2)

Note

Elements in a triplet (a,b,c) must be in non-descending order. (ie, a ≤ b ≤ c)

The solution set must not contain duplicate triplets.

Solution

Use 3 pointers:

• Sort the array.
• for each position i in the array:
  • skip if it is the same as the previous value (num[i] == num[i - 1]) to make sure the triplets are unique.
  • create a left pointer at i + 1 and a right pointer at n - 1.
  • if the sum of i, left and right is 0, add the triplet to the result.
  • if the sum is less than 0, move the left pointer to the right; otherwise move the right pointer to the left.
• return the result.

Complexity: The sort takes O(n log n) and the loop takes O(n^2), so the overall is O(n^2). Extra space is constant O(1).

Related Problems

• Two Sum
• 3Sum Closest
• 4Sum