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7. Maximum Subarray

easyAsked at Brex

Find the contiguous subarray with the largest sum and return that sum.

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

Problem

Given an integer array nums, find the contiguous subarray (containing at least one number) which has 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 = [1]
Output
1

Approaches

1. Brute force

Try every (i,j) subarray and track max sum.

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);}}

Tradeoff:

2. Kadane's algorithm

Track the best subarray ending at i: either extend or restart at nums[i]. Track global max.

Time
O(n)
Space
O(1)
function maxSubArray(nums) {
  let best = nums[0];
  let cur = 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:

Brex-specific tips

Brex frames Kadane as finding the worst rolling-window spend on a card timeline, so be ready to extend it to return the index range — auditors will ask which transactions caused the spike.

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