# Maximum Sum of Hourglass in Matrix | Solved in Java, Python

First of all, understand the Hourglass. It is shaped as shown in the below image.

There can be multiple hourglasses in the 2D array (matrix).

Problem Statement: Write a Python program to find the maximum sum of hourglass in matrix in Python and Java.

Explanation: Solving this problem includes finding all the hourglass and calculating the sum of every hourglass.

This is a coding challenge question. You can solve it in any programming language.

#### Python Program:

Let’s solve it in Python programming.

Prerequisite:

Python Code:

```arr =[
[1, 1, 1, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[1, 1, 1, 0, 0, 0],
[0, 0, 2, 4, 4, 0],
[0, 0, 0, 2, 0, 0],
[0, 0, 1, 2, 4, 0]]

#This function will return the sum of the hourglass
def sum_hg(x, y):
sum = arr[x][y] + arr[x][y+1] +arr[x][y+2]
sum = sum + arr[x+1][y+1]
sum = sum + arr[x+2][y]+arr[x+2][y+1]+arr[x+2][y+2]
return sum

size = len(arr)
sum = -63

for x in range(0, (size-2):
for y in range(0, (size-2):
k = sum_hg(x, y)
if k > sum:
sum = k

print("The largest sum of the HourGlass is ", sum)
```

Output:

`The largest sum of the HourGlass is 19.`

#### Java Program:

Now let’s try to solve this problem in Java programming.

Prerequisite:

Java Code:

```import java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;

public class HG_Class {
public static void main(String[] args) {
int[][] arr = {{1, 1, 1, 0, 0, 0},
{0, 1, 0, 0, 0, 0},
{1, 1, 1, 0, 0, 0},
{0, 0, 2, 4, 4, 0},
{0, 0, 0, 2, 0, 0},
{0, 0, 1, 2, 4, 0}};

int sum=-63;

for(int p=5; p>=2; p--) {
for(int q=5; q>=2; q--){

int  sum_hg = arr[p][q]+arr[p][q-1]+arr[p][q-2];
sum_hg += arr[p-1][q-1];
sum_hg += arr[p-2][q]+arr[p-2][q-1]+arr[p-2][q-2];

if(sum_hg>sum) sum=sum_hg;
}
}
System.out.println("Largest sum of the HourGlass is "+ sum);
}
}```

Output:

```Largest sum of the HourGlass is 19
```

This is how you can find maximum sum of hourglass in matrix. This question was asked in the HackerRank test. The level of the question is low.