17. Maximum Subarray

Topic :

arrays

Difficulty :

medium

Problem Link :

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) the solution, try coding another solution using the divide and conquer approach, which is more subtle.

solution

KADANE’S ALGORITHM

TIME COMPLEXITY : O(N)

SPACE COMPLEXITY : O(1)

// kadane's algorithm //
import java.io.*;
import java.util.*;
class MaximumSubarraySum
{ 
  static int maxSum(int a[])
    { int sum=0;
        int max=a[0];
        for(int i=0;i<a.length;i++)
        { sum=sum+a[i];
            max=Math.max(sum,max);  
            if(sum<0)
             sum=0;
           
        }        
    return max;
    }
  public static void main(String args[])
    {
        int a[]={-2,-3,4,-1,-2,1,5,-3};
        System.out.println(maxSum(a));
    }
}