0053 - Maximum Subarray

0053 - Maximum Subarray

Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum. A subarray is a contiguous part of an array.

Examples:

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

Input: nums = [1] Output: 1

Input: nums = [5,4,-1,7,8] Output: 23

Constraints:

1 <= nums.length <= 3 * 104 -105 <= nums[i] <= 105

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.

Java Solution

Dynamic Programming

class Solution {
    public int maxSubArray(int[] nums) {
        int max = nums[0];
        int tempMax = nums[0];
        for(int i = 1; i < nums.length; i++) {
            if(nums[i] > nums[i] + tempMax) tempMax = nums[i];
            else tempMax += nums[i];
            
            if(tempMax > max) max = tempMax;
        }
        
        return max;
    }
}

Brute Force

class Solution {
    public int maxSubArray(int[] nums) {
        int maxSubArray = Integer.MIN_VALUE;
        for(int i = 0; i < nums.length; i++) {
            int currentSubArray = 0;
            for(int j = i; j < nums.length; j++) {
                currentSubArray += nums[j];
                if(currentSubArray > maxSubArray) maxSubArray = currentSubArray;
            }
        }
        return maxSubArray;
    }
}