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apps/docs/content/(array)/15-3sum.mdx

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+---
+title: '15. 3Sum'
+description: 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
+sidebar:
+  label: '3Sum'
+  badge: 'Medium'
+---
+
+<Badge variant="accent">Two Pointers</Badge>
+
+::::warning
+Notice that the solution set must not contain duplicate triplets.
+::::
+
+### Example 1:
+- Input: `nums = [-1,0,1,2,-1,-4]`
+- Output: `[[-1,-1,2],[-1,0,1]]`
+- Explanation: `nums[0] + nums[1] + nums[2] = (-1) + 0 + 1 = 0`. `nums[1] + nums[2] + nums[4] = 0 + 1 + (-1) = 0`. `nums[0] + nums[3] + nums[4] = (-1) + 2 + (-1) = 0`. The distinct triplets are `[-1,0,1]` and `[-1,-1,2]`. Notice that the order of the output and the order of the triplets does not matter.
+
+### Example 2:
+- Input: `nums = [0,1,1]`
+- Output: `[]`
+- Explanation: The only possible triplet does not sum up to `0`.
+
+### Example 3:
+- Input: `nums = [0,0,0]`
+- Output: `[[0,0,0]]`
+- Explanation: The only possible triplet sums up to `0`.
+
+### Constraints:
+
+- `3 <= nums.length <= 3000`
+- `-10^5 <= nums[i] <= 10^5`
+
+## Solution
+
+```py
+class Solution:
+    def threeSum(self, nums: list[int]) -> list[list[int]]:
+        nums.sort()
+        result = []
+        n = len(nums)
+
+        for i in range(n):
+            # skip all zero
+            if i > 0 and nums[i] == nums[i - 1]:
+                continue
+
+            # two pointers
+            left = i + 1
+            right = n - 1
+            target = -nums[i]
+
+            while left < right:
+                current = nums[left] + nums[right]
+
+                if current == target:
+                    result.append([nums[i], nums[left], nums[right]])
+
+                    # skip duplicates
+                    while left < right and nums[left] == nums[left + 1]:
+                        left += 1
+                    while left < right and nums[right] == nums[right - 1]:
+                        right -= 1
+
+                    # shift pointers
+                    left += 1
+                    right -= 1
+
+                # since sorted, if current < target, then move left
+                elif current < target:
+                    left += 1
+                # since sorted, if current > target, then move right
+                else:
+                    right -= 1
+
+        return result
+```