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7. Maximum Subarray

easyAsked at GitHub

Find the contiguous subarray with the largest sum — GitHub uses this Kadane warmup before stepping into hunk-coalescing scoring in their diff renderer.

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

Problem

Given an integer array nums, find the contiguous subarray (containing at least one number) with the largest sum and return its sum.

Constraints

  • 1 <= nums.length <= 10^5
  • -10^4 <= nums[i] <= 10^4

Examples

Example 1

Input
nums = [-2,1,-3,4,-1,2,1,-5,4]
Output
6

Example 2

Input
nums = [5,4,-1,7,8]
Output
23

Approaches

1. Brute force

Try every (i,j) pair.

Time
O(n^2)
Space
O(1)
let best = -Infinity;
for (let i=0;i<n;i++){let s=0;for(let j=i;j<n;j++){s+=nums[j];best=Math.max(best,s);}}
return best;

Tradeoff:

2. Kadane

Track best-ending-here; either extend prior subarray or restart from the current element. Global max tracks the answer.

Time
O(n)
Space
O(1)
function maxSubArray(nums) {
  let cur = nums[0], best = nums[0];
  for (let i = 1; i < nums.length; i++) {
    cur = Math.max(nums[i], cur + nums[i]);
    best = Math.max(best, cur);
  }
  return best;
}

Tradeoff:

GitHub-specific tips

GitHub links this to hunk-similarity scoring in `git diff --patience` — the running maximum is exactly how they score contiguous match runs.

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