3Sum Closest

1. Sort the Array

• Sort nums in ascending order
• This enables the two-pointer technique by creating a predictable order

2. Initialize Closest Sum

• Set closest to the sum of the first three elements
• This gives us a valid starting comparison value

3. Iterate with a Fixed Pointer

• Loop index i from 0 to nums.length - 3
• For each i, the element nums[i] is fixed as the first of three numbers

4. Set Up Two Pointers

• Place left at i + 1
• Place right at the last index of the array
• These two pointers will scan inward to find the best pair

5. Compute the Three-Element Sum

• Calculate sum = nums[i] + nums[left] + nums[right]
• Compare |sum - target| with |closest - target|
• If the current sum is closer, update closest

6. Move Pointers Based on Comparison

• If sum < target: increment left to increase the sum
• If sum > target: decrement right to decrease the sum
• If sum === target: return immediately — exact match is the closest possible

7. Return the Result

• After all iterations, return closest
• This holds the three-element sum nearest to the target

Key Insight

Sorting the array transforms a brute-force O(n³) problem into an O(n²) solution. By fixing one element and using two pointers that move inward, we efficiently explore all meaningful triplet combinations without redundant checks.