sum_of_all_submatrices_3.cpp file added

Author: kiruba-r11

2D Arrays/sum_of_all_submatrices_3.cpp

@@ -0,0 +1,72 @@
+// Problem - Print the sum of all submatrices of the given matrix
+
+// Sample Input - 1
+//	3 3
+//	1 1 1
+//	1 1 1
+//	1 1 1
+
+// Sample Output - 1
+//	100
+
+// Sample Input - 2
+//	3 2
+//	1 10 8
+// -1 5 0
+
+// Sample Output - 2
+//	152
+
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+
+int sum_of_all_submatrices(vector <vector <int>> grid) {
+
+// Contribution of an element to the sum is defined as at index (i , j) of matrix with order n * m:
+//	value * (i + 1) * (j + 1) * (n - i) * (m - j)
+
+// Time Complexity: O(n ^ 2)
+// Auxiliary Space Complexity: O(1)
+
+
+int n = grid.size();
+int m = grid[0].size();
+int sum = 0;
+
+
+// Traversing the matrix
+for(int i = 0; i < n; i++) {
+for(int j = 0; j < m; j++) {
+
+// Calculating the contribution of an element to the sum and adding it to the sum
+sum += grid[i][j] * (i + 1) * (j + 1) * (n - i) * (m - j);
+}
+}
+
+return sum;
+
+}
+
+int main() {
+
+int m , n;
+cout << "Enter the no. of rows and columns : " << endl;
+cin >> m >> n;
+
+vector <vector <int>> grid(m , vector<int> (n));
+cout << "Enter the elements of the matrix : " << endl;
+for (int i = 0; i < m; i++) {
+for (int j = 0; j < n; j++) {
+cin >> grid[i][j];
+}
+}
+
+int sum = sum_all_submatrices(grid);
+
+cout << "The sum of all submatrices of the given matrix is : " << sum << endl;
+
+return 0;
+}