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7. Maximum Subarray

easyAsked at Nubank

Find the largest profitable contiguous period from a daily P&L series on a credit portfolio.

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.

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

Carry running sum; reset to nums[i] when it dips negative.

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

Nubank-specific tips

Nubank reviewers expect candidates to explain the negative-sum invariant out loud — they read it as a proxy for understanding monotonic accumulators in interest-accrual code.

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