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16. 3Sum

mediumAsked at Coupang

Find all unique triplets that sum to zero, mirroring how Coupang's bundle-pricing engine identifies SKU combinations that hit a target promotional discount during peak-event throughput.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given an array nums, return all unique triplets [a, b, c] such that a + b + c == 0. The solution set must not contain duplicate triplets.

Constraints

  • 3 <= nums.length <= 3000
  • -10^5 <= nums[i] <= 10^5

Examples

Example 1

Input
nums=[-1,0,1,2,-1,-4]
Output
[[-1,-1,2],[-1,0,1]]

Example 2

Input
nums=[0,1,1]
Output
[]

Approaches

1. Brute triple loop

Try all i<j<k and dedupe.

Time
O(n^3)
Space
O(n)
for i, for j>i, for k>j: if sum===0 push sorted triplet to a Set keyed by tuple;

Tradeoff:

2. Sort + two pointers

Sort, fix one element, then two-pointer scan for the remaining pair sum. Skip duplicates as you go.

Time
O(n^2)
Space
O(1) extra
function threeSum(nums) {
  nums.sort((a, b) => a - b);
  const out = [];
  for (let i = 0; i < nums.length - 2; i++) {
    if (i > 0 && nums[i] === nums[i - 1]) continue;
    let l = i + 1, r = nums.length - 1;
    while (l < r) {
      const s = nums[i] + nums[l] + nums[r];
      if (s === 0) {
        out.push([nums[i], nums[l], nums[r]]);
        while (l < r && nums[l] === nums[l + 1]) l++;
        while (l < r && nums[r] === nums[r - 1]) r--;
        l++; r--;
      } else if (s < 0) l++;
      else r--;
    }
  }
  return out;
}

Tradeoff:

Coupang-specific tips

Coupang's bundle-pricing engine identifies SKU combinations that hit a target promotional discount during peak-event throughput; the sort + two-pointer pattern is the standard for combinatorial pricing checks at sub-quadratic cost.

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Output

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