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

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

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.

Method 0. dp
class Solution {
    public int maxSubArray(int[] nums) {
        int[] dp = new int[nums.length];
        dp[0] = nums[0];
        int max = nums[0];
        for(int i = 1; i < nums.length; i++) {
            dp[i] = Math.max(dp[i-1] + nums[i], nums[i]);
            max = Math.max(dp[i], max);
        }
        return max;
    }
}

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

            if(sum > max) {
                max = sum;
            }
        }
        return max;
    }
}


Method 2.
class Solution {
    public int maxSubArray(int[] nums) {
        if(nums.length == 1) return nums[0];
        int sum = nums[0];
        int max = nums[0];
        for(int i = 1; i < nums.length; i++) {
            sum = Math.max(nums[i], sum + nums[i]);
            max = Math.max(max, sum);
        }
        return max;
    }
}