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7. Maximum Subarray

easyAsked at Coursera

Find the contiguous subarray with the largest sum — Coursera uses this to test Kadane in a learner-engagement streak setting.

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

Sum every subarray and track max.

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

Reset running sum to nums[i] whenever it'd otherwise hurt.

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:

Coursera-specific tips

Coursera frames this as picking the best contiguous week-window of learner-engagement deltas — naming the DP state in domain terms scores extra points.

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