3Sum

Problem

Given an integer array nums, return all the triplets [nums[i], nums[j], nums[k]] such that i != j, i != k, and j != k, and nums[i] + nums[j] + nums[k] == 0.

The solution set must not contain duplicate triplets.

Input / Output Format

Input: Array of integers nums. Output: List of unique triplets summing to zero (any order).

Examples

Example 1

Input: nums = [-1, 0, 1, 2, -1, -4] Output: [[-1, -1, 2], [-1, 0, 1]] Explanation: Distinct triplets summing to 0 are (-1, -1, 2) and (-1, 0, 1). Other combos either repeat or don't sum to 0.

Example 2

Input: nums = [0, 1, 1] Output: [] Explanation: No triplet sums to 0.

Example 3

Input: nums = [0, 0, 0] Output: [[0, 0, 0]] Explanation: Single valid triplet.

Approach Hints

• Sort + Two Pointers — Sort nums. Fix index i, then two pointers l = i+1, r = n-1 scan for pairs summing to -nums[i]. Skip duplicates at all three levels. Time: O(n²), Space: O(1) extra.
• Hash Set — For each pair (i,j), look up -(nums[i]+nums[j]). Harder to dedupe; sort-based is cleaner.
• Duplicate skipping is the trickiest part — advance i past equal values; after a hit, advance l and r past equal values too.