[feature-1] Added sum of all sub matrices 2 in CPP

2D Arrays/sum_of_all_submatrices_2.cpp

@@ -0,0 +1,91 @@
+// 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_all_submatrices(vector <vector <int>> grid) {
+
+	int n = grid.size();
+	int m = grid[0].size();
+	int sum = 0;
+
+	vector <vector <int>> prefix(n , vector <int> (m));
+
+	for (int i = 0; i < n; i++) {
+		for (int j = 0; j < m; j++) {
+			if (j == 0)
+				prefix[i][j] = grid[i][j];
+			else
+				prefix[i][j] = prefix[i][j - 1] + grid[i][j];
+		}
+	}
+
+	for (int i = 0; i < n; i++) {
+		for (int j = 0; j < m; j++) {
+			if (i != 0)
+				prefix[i][j] += prefix[i - 1][j];
+		}
+	}
+
+	for (int i = 0; i < n; i++) {
+		for (int j = 0; j < m; j++) {
+			for (int tl = i; tl < n; tl++) {
+				for (int br = j; br < m; br++) {
+
+					sum += (prefix[tl][br]);
+
+					if (i > 0 && j > 0)
+						sum = sum - (prefix[tl][j - 1] + prefix[i - 1][br]) + prefix[i - 1][j - 1];
+					else if (i > 0)
+						sum = sum - prefix[i - 1][br];
+					else
+						sum = sum - prefix[tl][j - 1];
+				}
+			}
+		}
+	}
+
+	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;
+
+}