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3Sum Closest

Medium·LeetCode #16 Pro OnlySlight Variation
LeetCode
01

Problem Statement

You are given an integer array nums and a number target.

Pick three elements from three different positions. Among all such triplets, find the one whose sum is closest to target, and return that sum.

You may assume there is exactly one closest sum.

Input

An integer array nums and an integer target.

Output

One integer: the triplet sum with the smallest |sum − target|.

Example 1
Input: nums = [-1, 2, 1, -4], target = 1
Output: 2

−1 + 2 + 1 = 2 is only 1 away from the target. No triplet sums to exactly 1.

Example 2
Input: nums = [0, 0, 0], target = 1
Output: 0

The only triplet adds up to 0.

Constraints
  • • 3 ≤ nums.length ≤ 500
  • • −1000 ≤ nums[i] ≤ 1000
  • • −10^4 ≤ target ≤ 10^4
02

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“three integers”
→ Fix one, pair the other two → k-sum family.
“closest to target”
→ No exact match to find, so keep a running best. The sign of `sum − target` still says which pointer to move.
“return the sum”
→ Positions don't matter, so sorting is fine.
03

Approach Complexity Ladder

Brute Force — every tripletO(N³)O(1)

Three loops; keep the sum with the smallest distance

Better — sort, fix two, binary search the thirdO(N² · log N)O(1)

Sort; for each pair, binary search the value closest to what's left

Optimal — sort, fix one, two pointersO(N²)O(1)

Sort; fix nums[i]; move left/right towards the target, track the closest

Brute Force Intuition

Check every triplet i < j < k. Keep the sum whose distance |sum − target| is smallest.

Recognition rule for this sub-pattern:

Sort, fix one element (or more), and solve the rest as a two-pointer pair problem. Skip duplicates carefully.
Remember this · Two Pointers
Trigger
Sorted array, pairs/triplets with a target, comparing from both ends, compacting an array in place.
Think
If I compare the elements at two positions, can I safely discard one side?
Key question
Which pointer moves, and why can the skipped elements never be the answer?
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3SumValid Triangle Number