Is Maximum Subarray easy or hard?

Maximum Subarray is generally considered a medium-level problem. The brute force idea is simple, but recognizing Kadane's Algorithm and understanding why resetting the running sum works requires algorithmic insight.

How to solve Maximum Subarray in O(n)?

Use Kadane's Algorithm. Maintain a running sum that represents the best subarray ending at the current index, calculated as max(nums[i], current_sum + nums[i]). Track the global maximum during iteration to get the final answer in linear time.

What is the best approach for Maximum Subarray?

Kadane's Algorithm is the best approach. It processes the array in a single pass while maintaining the maximum subarray ending at each position. The algorithm runs in O(n) time and O(1) space, which is optimal for this problem.

What data structure is used in Maximum Subarray?

The problem primarily uses an array as the input structure. The optimal solution does not require additional data structures, only a few variables to track running sums and the current maximum.

What is the time complexity of Maximum Subarray?

The optimal solution using Kadane's Algorithm runs in O(n) time because each element is processed exactly once. The divide and conquer approach runs in O(n log n) due to recursive splitting and merging of subarray results.

Maximum Subarray Python or Java solution approach?

Most Python and Java implementations use Kadane's Algorithm. Iterate through the array, update the running sum with max(current + num, num), and keep a global maximum variable. This keeps the implementation short and runs in O(n) time.

Is Maximum Subarray asked at Google, Amazon, or Meta?

Maximum Subarray is a classic interview problem frequently asked by companies like Google, Amazon, Meta, and Microsoft. It tests dynamic programming intuition, array manipulation, and the ability to optimize brute force approaches into linear-time solutions.

Description Solution Video 8:03

53. Maximum Subarray

Medium53.7% acceptance64 companies

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.