# Count rows/columns with sum equals to diagonal sum

Given an n x n square matrix, count all rows and columns whose sum is equal to the sum of any principal diagonal or secondary diagonal.

Examples:

```Input : n = 3
arr[][] = { {1, 2, 3},
{4, 5, 2},
{7, 9, 10}};
Output : 2
In first example sum of principal diagonal
= (1 + 5 + 10) = 16  and sum of secondary
diagonal = (3 + 5 + 7) = 15.

Input:  n = 4
arr[][] =  { { 7, 2, 3, 5 },
{ 4, 5, 6, 3 },
{ 7, 9, 10, 12 },
{ 1, 5, 4, 3 } };
Output: 1
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

We need to count number of rows or columns whose sum is equal to 16 or 15. So find sum of all rows and columns and if their sum is equal to 16 or 15 then increment the count.
Therefore, sum of column {2, 5, 9} = 16 and sum column {3, 2, 10} = 15. Hence, the count is equal to 2.

 `// C++ program to Count number of rows and ` `// columns having sum is equal to sum of  ` `// any diagonal in matrix ` `#include ` `#define n 4 ` `using` `namespace` `std; ` ` `  ` `  `// function to count number of rows countnd columns ` `// whose sum is equal to sum of any diagonal ` `int` `count(``int` `arr[][n]) ` `{ ` `    ``int` `diag1 = 0, diag2 = 0; ` `    ``int` `row = 0, col = 0, count = 0; ` ` `  `    ``for` `(``int` `i = 0, j = n - 1; i < n; i++, j--) ` `    ``{ ` `        ``// sum of principle diagonal ` `        ``diag1 += arr[i][i]; ` ` `  `        ``// sum of secondary diagonal ` `        ``diag2 += arr[i][j]; ` `    ``} ` ` `  `    ``// Find the sum of individual ` `    ``// row and column ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``row = 0, col = 0; ` `         `  `        ``for` `(``int` `j = 0; j < n; j++) { ` `            ``row = row + arr[i][j]; ` `        ``} ` `        ``for` `(``int` `j = 0; j < n; j++) { ` `            ``col = col + arr[j][i]; ` `        ``} ` `        ``if` `((row == diag1) || (row == diag2)) { ` `            ``count++; ` `        ``} ` `        ``if` `((col == diag1) || (col == diag2)) ` `            ``count++; ` `    ``} ` `     `  `    ``return` `count; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[n][n] = { { 7, 2, 3, 5 }, ` `                    ``{ 4, 5, 6, 3 }, ` `                    ``{ 7, 9, 10, 12 }, ` `                    ``{ 1, 5, 4, 3 } };     ` `    ``cout << count(arr) << endl; ` `} `

 `// Java program to Count number of rows and ` `// columns having sum is equal to sum of ` `// any diagonal in matrix ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` ` `  `    ``static` `int` `n = ``4``; ` `     `  `    ``// function to count number of rows countnd  ` `    ``// columns whose sum is equal to sum of any ` `    ``// diagonal ` `    ``static` `int` `count(``int` `arr[][]) ` `    ``{ ` `         `  `        ``int` `diag1 = ``0``, diag2 = ``0``; ` `        ``int` `row = ``0``, col = ``0``, count = ``0``; ` ` `  `        ``for` `(``int` `i = ``0``, j = n - ``1``; i < n; i++, j--)  ` `        ``{ ` `             `  `            ``// sum of principle diagonal ` `            ``diag1 += arr[i][i]; ` ` `  `            ``// sum of secondary diagonal ` `            ``diag2 += arr[i][j]; ` `        ``} ` ` `  `        ``// Find the sum of individual ` `        ``// row and column ` `        ``for` `(``int` `i = ``0``; i < n; i++) { ` `            ``row = ``0``; ` `            ``col = ``0``; ` ` `  `            ``for` `(``int` `j = ``0``; j < n; j++) { ` `                ``row = row + arr[i][j]; ` `            ``} ` `             `  `            ``for` `(``int` `j = ``0``; j < n; j++) { ` `                ``col = col + arr[j][i]; ` `            ``} ` `             `  `            ``if` `((row == diag1) || (row == diag2))  ` `                ``count++; ` `             `  `            ``if` `((col == diag1) || (col == diag2)) ` `                ``count++; ` `        ``} ` ` `  `        ``return` `count; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[][] = {{``7``, ``2``, ``3``, ``5``}, ` `                        ``{``4``, ``5``, ``6``, ``3``}, ` `                        ``{``7``, ``9``, ``10``, ``12``}, ` `                        ``{``1``, ``5``, ``4``, ``3``}}; ` `                         `  `        ``System.out.println(count(arr)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

 `# Python3 program to Count number of rows  ` `# and columns having sum is equal to sum   ` `# of any diagonal in matrix ` `n ``=` `4` ` `  `# Function to count number of rows ` `# countnd columns whose sum is equal ` `# to sum of any diagonal ` `def` `count(arr): ` `    ``diag1 ``=` `0``; diag2 ``=` `0``; row ``=` `0` `    ``col ``=` `0``; count ``=` `0``; j ``=` `n ``-` `1` `     `  `    ``for` `i ``in` `range``(n): ` `     `  `        ``# sum of principle diagonal ` `        ``diag1 ``+``=` `arr[i][i] ` ` `  `        ``# sum of secondary diagonal ` `        ``diag2 ``+``=` `arr[i][j] ` `        ``j ``-``=` `1` `     `  ` `  `    ``# Find the sum of individual ` `    ``# row and column ` `    ``for` `i ``in` `range``(n): ` `        ``row ``=` `0``; col ``=` `0` `         `  `        ``for` `j ``in` `range``(n): ` `            ``row ``+``=` `arr[i][j] ` `         `  `        ``for` `j ``in` `range``(n): ` `            ``col ``+``=`  `arr[j][i] ` `         `  `        ``if` `((row ``=``=` `diag1) ``or` `(row ``=``=` `diag2)): ` `            ``count ``+``=` `1` `         `  `        ``if` `((col ``=``=` `diag1) ``or` `(col ``=``=` `diag2)): ` `            ``count ``+``=` `1` `     `  `    ``return` `count ` ` `  `# Driver code ` ` `  `arr ``=` `[[ ``7``, ``2``, ``3``, ``5` `], ` `      ``[ ``4``, ``5``, ``6``, ``3` `], ` `      ``[ ``7``, ``9``, ``10``, ``12` `], ` `      ``[ ``1``, ``5``, ``4``, ``3` `] ]  ` `print``(count(arr)) ` ` `  `# This code is contributed by Anant Agarwal. `

 `// C# program to Count number of rows and ` `// columns having sum is equal to sum of ` `// any diagonal in matrix ` `using` `System; ` ` `  `namespace` `Matrix ` `{ ` `public` `class` `GFG ` `{      ` `     `  `static` `int` `n = 4; ` `     `  `    ``// Function to count number of rows   ` `    ``// countnd columns whose sum is equal  ` `    ``// to sum of any diagonal ` `    ``static` `int` `count(``int` `[,]arr) ` `    ``{ ` `         `  `        ``int` `diag1 = 0, diag2 = 0; ` `        ``int` `row = 0, col = 0, count = 0; ` ` `  `        ``for` `(``int` `i = 0, j = n - 1; i < n; i++, j--)  ` `        ``{ ` `             `  `            ``// sum of principle diagonal ` `            ``diag1 += arr[i,i]; ` ` `  `            ``// sum of secondary diagonal ` `            ``diag2 += arr[i,j]; ` `        ``} ` ` `  `        ``// Find the sum of individual ` `        ``// row and column ` `        ``for` `(``int` `i = 0; i < n; i++) { ` `            ``row = 0; ` `            ``col = 0; ` ` `  `            ``for` `(``int` `j = 0; j < n; j++) { ` `                ``row = row + arr[i,j]; ` `            ``} ` `             `  `            ``for` `(``int` `j = 0; j < n; j++) { ` `                ``col = col + arr[j,i]; ` `            ``} ` `             `  `            ``if` `((row == diag1) || (row == diag2))  ` `                ``count++; ` `             `  `            ``if` `((col == diag1) || (col == diag2)) ` `                ``count++; ` `        ``} ` ` `  `        ``return` `count; ` `    ``} ` ` `  ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[,]arr = {  { 7, 2, 3, 5 }, ` `                        ``{ 4, 5, 6, 3 }, ` `                        ``{ 7, 9, 10, 12 }, ` `                        ``{ 1, 5, 4, 3 } };  ` `        ``Console.Write(count(arr)); ` `    ``} ` `}  ` `} ` ` `  ` `  `// This code is contributed by Sam007 `

 ` `

Output:

`1`

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