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7. Maximum Subarray

easyAsked at Expedia

Find the contiguous subarray with the largest 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. All subarrays

Compute sums of every contiguous range.

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

Tradeoff:

2. Kadane's algorithm

Track running sum, reset when it goes negative. Expedia uses this pattern for max-profit booking windows.

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:

Expedia-specific tips

Expedia interviewers often pivot to 'max-profit booking window' framing — be ready to explain how Kadane's translates to identifying peak booking-revenue streaks.

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