053. Maximum Subarray

At a Glance

• Topic: Dynamic Programming
• Pattern: Kadane's Algorithm
• Difficulty: Medium
• LeetCode: 053

Problem Statement

Given an integer array nums, find the subarray with the largest sum, and return its sum.

Example 1:

Input: nums = [-2,1,-3,4,-1,2,1,-5,4] Output: 6 Explanation: The subarray [4,-1,2,1] has the largest sum 6.

Example 2:

Input: nums = [1] Output: 1 Explanation: The subarray [1] has the largest sum 1.

Example 3:

Input: nums = [5,4,-1,7,8] Output: 23 Explanation: The subarray [5,4,-1,7,8] has the largest sum 23.

Constraints:

1 <= nums.length <= 105
-104 <= nums[i] <= 104

Follow up: If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

Approach & Solution Steps

Use Kadane's Algorithm. Keep a running sum. If the running sum becomes negative, reset it to zero (or the current element). Keep track of the maximum sum seen so far.

Optimal JS Solution

function maxSubArray(nums) {
  let maxSum = -Infinity;
  let currentSum = 0;
  for (const num of nums) {
    currentSum = Math.max(num, currentSum + num);
    maxSum = Math.max(maxSum, currentSum);
  }
  return maxSum;
}

Edge Cases & Pitfalls

• Always consider empty or null inputs.
• Watch out for off-by-one index errors.