# Check if two elements of a matrix are on the same diagonal or not

Given a matrix mat[][], and two integers X and Y, the task is to check if X and Y are on the same diagonal of the given matrix or not.

Examples:

Input: mat[][]= {{1, 2}. {3, 4}}, X = 1, Y = 4
Output: Yes
Explanation:
Both X and Y lie on the same diagonal.

Input: mat[][]= {{1, 2}. {3, 4}}, X = 2, Y = 4
Output: No

Approach: The key observation to solve the problem is that the two elements of the matrix are on the same diagonal only if the sum of the indices or the absolute difference of the indices of the elements are equal. Follow the steps below to solve the problem:

• Traverse the matrix and find the indices of the elements of the matrix.
• Check if the elements are on the same diagonal.
Let the indices of the elements of the matrix are (P, Q) and (X, Y), then the condition that both the elements are on the same diagonal is given by the following equation:

abs(P – Q) == abs(X – Y) or P + Q == X + Y

• If the above condition is satisfied, print “Yes”. Otherwise, print “No”.

Below is the implementation of the above approach:

## C++

 `// C++ program for ` `// the above approach` `#include ` `using` `namespace` `std;`   `// Function to check if two` `// integers are on the same` `// diagonal of the matrix` `void` `checkSameDiag(``int` `li, ``int` `x,` `                   ``int` `y, ``int` `m, ``int` `n) ` `{` `  ``// Storing indexes of x in I, J` `  ``int` `I = 0, J = 0;`   `  ``// Storing Indexes of y in P, Q` `  ``int` `P = 0, Q = 0;`   `  ``for``(``int` `i = 0; i < m; i++)` `  ``{` `    ``for``(``int` `j = 0; j < n; j++) ` `    ``{` `      ``if` `(li[i][j] == x)` `      ``{` `        ``I = i;` `        ``J = j;` `      ``}` `      ``if` `(li[i][j] == y)` `      ``{` `        ``P = i;` `        ``Q = j;` `      ``}` `    ``}` `  ``}`   `  ``// Condition to check if the` `  ``// both the elements are in` `  ``// same diagonal of a matrix` `  ``if` `(``abs``(P - Q) == ``abs``(I - J) ||` `      ``P + Q == I + J) ` `  ``{` `    ``cout << ``"YES"``;` `  ``} ` `  ``else` `    ``cout << ``"NO"``;` `}`   `// Driver code` `int` `main() ` `{` `  ``// Dimensions of Matrix` `  ``int` `m = 6;` `  ``int` `n = 5;`   `  ``// Given Matrix` `  ``int` `li = {{32, 94, 99, 26, 82},` `                  ``{51, 69, 52, 63, 17},` `                  ``{90, 36, 88, 55, 33},` `                  ``{93, 42, 73, 39, 28},` `                  ``{81, 31, 83, 53, 10},` `                  ``{12, 29, 85, 80, 87}};`   `  ``// Elements to be checked` `  ``int` `x = 42;` `  ``int` `y = 80;`   `  ``// Function call` `  ``checkSameDiag(li, x, y, m, n);` `  ``return` `0;` `}`   `//This code is contributed by 29AjayKumar`

## Java

 `// Java implementation of the ` `// above approach` `class` `GFG{` `    `  `// Function to check if two` `// integers are on the same` `// diagonal of the matrix` `static` `void` `checkSameDiag(``int` `li[][], ``int` `x,` `                          ``int` `y, ``int` `m, ``int` `n) ` `{` `    `  `    ``// Storing indexes of x in I, J` `    ``int` `I = ``0``, J = ``0``;` `    `  `    ``// Storing Indexes of y in P, Q` `    ``int` `P = ``0``, Q = ``0``;` `    `  `    ``for``(``int` `i = ``0``; i < m; i++)` `    ``{` `        ``for``(``int` `j = ``0``; j < n; j++) ` `        ``{` `            ``if` `(li[i][j] == x)` `            ``{` `                ``I = i;` `                ``J = j;` `            ``}` `            ``if` `(li[i][j] == y)` `            ``{` `                ``P = i;` `                ``Q = j;` `            ``}` `        ``}` `    ``}` `    `  `    ``// Condition to check if the` `    ``// both the elements are in` `    ``// same diagonal of a matrix` `    ``if` `(Math.abs(P - Q) == Math.abs(I - J) ||` `        ``P + Q == I + J) ` `    ``{` `        ``System.out.println(``"YES"``);` `    ``} ` `    ``else` `        ``System.out.println(``"NO"``);` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    `  `    ``// Dimensions of Matrix` `    ``int` `m = ``6``;` `    ``int` `n = ``5``;`   `    ``// Given Matrix` `    ``int``[][] li = { { ``32``, ``94``, ``99``, ``26``, ``82` `},` `                   ``{ ``51``, ``69``, ``52``, ``63``, ``17` `},` `                   ``{ ``90``, ``36``, ``88``, ``55``, ``33` `},` `                   ``{ ``93``, ``42``, ``73``, ``39``, ``28` `},` `                   ``{ ``81``, ``31``, ``83``, ``53``, ``10` `},` `                   ``{ ``12``, ``29``, ``85``, ``80``, ``87` `} };`   `    ``// Elements to be checked` `    ``int` `x = ``42``;` `    ``int` `y = ``80``;`   `    ``// Function call` `    ``checkSameDiag(li, x, y, m, n);` `}` `}`   `// This code is contributed by Amit Katiyar`

## Python3

 `# Python3 implementation of the ` `# above approach`   `# Function to check if two ` `# integers are on the same ` `# diagonal of the matrix` `def` `checkSameDiag(x, y):` `    `  `    ``# Storing indexes of x in I, J` `    ``# Storing Indexes of y in P, Q` `    ``for` `i ``in` `range``(m):` `        ``for` `j ``in` `range``(n):` `            ``if` `li[i][j] ``=``=` `x:` `                ``I, J ``=` `i, j` `            ``if` `li[i][j] ``=``=` `y:` `                ``P, Q ``=` `i, j` `                `  `    ``# Condition to check if the ` `    ``# both the elements are in ` `    ``# same diagonal of a matrix` `    ``if` `abs``(P``-``Q) ``=``=` `abs``(I``-``J) ``or` `P ``+` `Q ``=``=` `I ``+` `J:` `        ``print``(``"YES"``)` `    ``else``:` `        ``print``(``"NO"``)`     `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:` `    `  `    ``# Dimensions of Matrix` `    ``m, n ``=` `6``, ``5` `    `  `    ``# Given Matrix` `    ``li ``=` `[[``32``, ``94``, ``99``, ``26``, ``82``],` `        ``[``51``, ``69``, ``52``, ``63``, ``17``],` `        ``[``90``, ``36``, ``88``, ``55``, ``33``],` `        ``[``93``, ``42``, ``73``, ``39``, ``28``],` `        ``[``81``, ``31``, ``83``, ``53``, ``10``],` `        ``[``12``, ``29``, ``85``, ``80``, ``87``]]` `    `  `    ``# elements to be checked` `    ``x, y ``=` `42``, ``80` `    `  `    ``# Function Call` `    ``checkSameDiag(x, y)`

## C#

 `// C# implementation of the ` `// above approach` `using` `System;` `class` `GFG{` `    `  `// Function to check if two` `// integers are on the same` `// diagonal of the matrix` `static` `void` `checkSameDiag(``int` `[,]li, ``int` `x,` `                          ``int` `y, ``int` `m, ``int` `n) ` `{` `  ``// Storing indexes of x in I, J` `  ``int` `I = 0, J = 0;`   `  ``// Storing Indexes of y in P, Q` `  ``int` `P = 0, Q = 0;`   `  ``for``(``int` `i = 0; i < m; i++)` `  ``{` `    ``for``(``int` `j = 0; j < n; j++) ` `    ``{` `      ``if` `(li[i, j] == x)` `      ``{` `        ``I = i;` `        ``J = j;` `      ``}` `      ``if` `(li[i, j] == y)` `      ``{` `        ``P = i;` `        ``Q = j;` `      ``}` `    ``}` `  ``}`   `  ``// Condition to check if the` `  ``// both the elements are in` `  ``// same diagonal of a matrix` `  ``if` `(Math.Abs(P - Q) == Math.Abs(I - J) ||` `                         ``P + Q == I + J) ` `  ``{` `    ``Console.WriteLine(``"YES"``);` `  ``} ` `  ``else` `    ``Console.WriteLine(``"NO"``);` `}`   `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `  ``// Dimensions of Matrix` `  ``int` `m = 6;` `  ``int` `n = 5;`   `  ``// Given Matrix` `  ``int` `[,]li = {{32, 94, 99, 26, 82},` `               ``{51, 69, 52, 63, 17},` `               ``{90, 36, 88, 55, 33},` `               ``{93, 42, 73, 39, 28},` `               ``{81, 31, 83, 53, 10},` `               ``{12, 29, 85, 80, 87}};`   `  ``// Elements to be checked` `  ``int` `x = 42;` `  ``int` `y = 80;`   `  ``// Function call` `  ``checkSameDiag(li, x, y, m, n);` `}` `} `   `// This code is contributed by 29AjayKumar`

Output:

```YES

```

Time Complexity: O(N * M)
Auxiliary Space: O(1)

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