This problem can be solved use several different algorithmic techniques, including brute force, divide and conquer, dynamic programming, and reduction to shortest paths. If the array contains all non-positive numbers, then a solution is any subarray of size 1 containing the maximal value of the array (or the empty subarray, if it is allowed). The maximal subarray problem was proposed by Ulf Grenander in 1977 as a simplified model for maximal likelihood estimate of shapes in digitized pictures. There is some evidence that no significantly faster algorithm exists; an algorithm that solves the two-dimensional maximal subarray problem in O(n3−ε) time, for any ε>0, would imply a similarly fast algorithm for the all-pairs shortest paths problem. Grenander derived an algorithm that solves the one-dimensional problem in O(n2) time, better the brute force working time of O(n3).

COMING SOON!

```
package DynamicProgramming;
import java.util.Scanner;
/**
* Program to implement Kadane’s Algorithm to
* calculate maximum contiguous subarray sum of an array
* Time Complexity: O(n)
*
* @author Nishita Aggarwal
*/
public class KadaneAlgorithm {
/**
* This method implements Kadane's Algorithm
*
* @param arr The input array
* @return The maximum contiguous subarray sum of the array
*/
static int largestContiguousSum(int arr[]) {
int i, len = arr.length, cursum = 0, maxsum = Integer.MIN_VALUE;
if (len == 0) //empty array
return 0;
for (i = 0; i < len; i++) {
cursum += arr[i];
if (cursum > maxsum) {
maxsum = cursum;
}
if (cursum <= 0) {
cursum = 0;
}
}
return maxsum;
}
/**
* Main method
*
* @param args Command line arguments
*/
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n, arr[], i;
n = sc.nextInt();
arr = new int[n];
for (i = 0; i < n; i++) {
arr[i] = sc.nextInt();
}
int maxContSum = largestContiguousSum(arr);
System.out.println(maxContSum);
sc.close();
}
}
```