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.


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

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


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.


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).

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