LeetCode - 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.

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.

Java Solution :

class Solution {

    public int maxSubArray(int[] nums) {

        int dp[] = new int[nums.length];

        dp[0] = nums[0];

        for(int i=1;i<nums.length;i++){

            dp[i] = Math.max(dp[i-1] + nums[i],nums[i]);

        }

        int maxValue = dp[0];

        for(int i = 1;i < nums.length;i++){

            maxValue = Math.max(maxValue,dp[i]);

        }

        return maxValue;

    }

}

Time Complexity : O(n)

Space Complexity: O(n) because we are using an array of size n.

Second Solution :

class Solution {

    public int maxSubArray(int[] nums) {

        int maxValue = nums[0];

        for(int i=1;i<nums.length;i++){

            nums[i] = Math.max(nums[i-1] + nums[i],nums[i]);

        }

        for(int i = 1;i < nums.length;i++){

            maxValue = Math.max(maxValue,nums[i]);

        }

        return maxValue;

    }

}

Time Complexity : O(n)

Space Complexity : O(1)

Python Posts:

MaxSubArray Python (LeetCode)