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Maximum sum of hour glass in matrix in C++
In this problem, we are given a matrix. Our task is to create a program that finds the maximum sum of the hourglass in a matrix in C++.
Program description − Here, we will find the maximum sum of all hourglasses that can be created for the given matrix elements.
Hour glass is a 7 element shape made in the matrix in the following form,
X X X X X X X
Let’s take an example to understand the problem,
Input −
array ={
{2 4 0 0}
{0 1 1 0}
{4 2 1 0}
{0 3 0 1}}Output −
Explanation −
Hour glass are : 2 4 0 0 1 1 1 2 4 2 1 0 3 0 4 0 0 1 1 0 1 1 2 1 0 3 0 1
So, an hourglass can be created using the following indexes,
matrix[i][j] matrix[i][j+1] matrix[i][j+2] matrix[i+1][j+1] matrix[i+2][j] matrix[i+2][j+1] matrix[i+2][j+2]
We will find the sum of all these elements of the array from [0][0] to [R2][C-2] starting points. And the find the maxSum for all these hourglasses created from array elements.
Example
Program to illustrate the working of our solution,
#include<iostream>
using namespace std;
const int row = 4;
const int col = 4;
int findHourGlassSum(int mat[row][col]){
if (row<3 || col<3)
return -1;
int maxSum = 0;
for (int i=0; i<row-2; i++){
for (int j=0; j<col-2; j++){
int hrSum = (mat[i][j]+mat[i][j+1]+mat[i][j+2])+ (mat[i+1][j+1])+ (mat[i+2][j]+mat[i+2][j+1]+mat[i+2][j+2]);
maxSum = max(maxSum, hrSum);
}
}
return maxSum;
}
int main() {
int mat[row][col] = {
{2, 4, 0, 0},
{0, 1, 1, 0},
{4, 2, 1, 0},
{0, 3, 0, 1}};
int maxSum = findHourGlassSum(mat);
if (maxSum == -1)
cout<<"Not possible";
else
cout<<"Maximum sum of hour glass created is "<<maxSum;
return 0;
}Output
Maximum sum of hour glass created is 14
Updated on: 03-Jun-2020
366 Views
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