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8. Maximum Subarray

mediumAsked at Adyen

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

Approaches

1. Brute force

Sum every subarray.

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

Tradeoff:

2. Kadane's algorithm

Carry the best subarray ending at i; reset when negative.

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:

Adyen-specific tips

Adyen maps Kadane's reset rule to multi-currency net-settlement windows — they expect you to articulate why you'd never carry a negative running sum across boundaries.

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