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# Construct a square Matrix whose parity of diagonal sum is same as size of matrix

• Last Updated : 08 Apr, 2021

Given an integer N representing the size of the matrix, the task is to construct a square matrix N * N which have an element from 1 to N2 such that the parity of the sum of its diagonals is equal to the parity of integer N.

Examples:

Input: N = 4
Output:
1   2   3   4
8   7   6   5
9  10  11 12
16 15 14 13
Explanation:
Sum of diagonal = 32 and 36 and integer N = 4, all the numbers are even that is same parity.

Input: N = 3
Output:
1 2 3
6 5 4
7 8 9
Explanation:
Sum of diagonal = 15 and integer N = 3, all the numbers are odd that is same parity.

Approach: The idea is to observe that on filling the elements in the matrix in an alternative fashion the parity of N and the sum of diagonals is the same. Start the counter from 1 and then fill the first row from 0 to N – 1 in increasing order, then fill the second row from index N – 1 to 0, and so on. Keep filling each element from value 1 to N2 in this alternate fashion to get the required matrix.
Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include``using` `namespace` `std;` `// Function to construct a N * N``// matrix based on the given condition``void` `createMatrix(``int` `N)``{``    ``// Matrix with given sizM``    ``int` `M[N][N];` `    ``// Counter to insert elements``    ``// from 1 to N * N``    ``int` `count = 1;``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``// Check if it is first row``        ``// or odd row of the matrix``        ``if` `(i % 2 == 0) {` `            ``for` `(``int` `j = 0; j < N; j++) {``                ``M[i][j] = count;``                ``count++;``            ``}``        ``}``        ``else``        ``{``            ``// Insert elements from``            ``// right to left``            ``for` `(``int` `j = N - 1;j >= 0; j--){``                ``M[i][j] = count;``                ``count += 1;``            ``}``        ``}``    ``}` `    ``// Print the matrix``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``// Traverse column``        ``for` `(``int` `j = 0; j < N; j++) {``            ``cout << M[i][j] << ``" "``;``        ``}``        ``cout << endl;``    ``}``}` `// Driver Code``int` `main()``{``    ``// Given size of matrix N``    ``int` `N = 3;` `    ``// Function Call``    ``createMatrix(N);``    ``return` `0;``}`

## Java

 `// Java program for the above approach``class` `GFG{`` ` `// Function to construct a N * N``// matrix based on the given condition``static` `void` `createMatrix(``int` `N)``{``    ``// Matrix with given sizM``    ``int` `M[][] = ``new` `int``[N][N];`` ` `    ``// Counter to insert elements``    ``// from 1 to N * N``    ``int` `count = ``1``;``    ``for` `(``int` `i = ``0``; i < N; i++)``    ``{`` ` `        ``// Check if it is first row``        ``// or odd row of the matrix``        ``if` `(i % ``2` `== ``0``)``        ``{`` ` `            ``for` `(``int` `j = ``0``; j < N; j++)``            ``{``                ``M[i][j] = count;``                ``count++;``            ``}``        ``}``        ``else``        ``{``            ``// Insert elements from``            ``// right to left``            ``for``(``int` `j = N - ``1``; j >= ``0``; j--){``                ``M[i][j] = count;``                ``count += ``1` `;``            ``}``        ``}``    ``}`` ` `    ``// Print the matrix``    ``for` `(``int` `i = ``0``; i < N; i++)``    ``{`` ` `        ``// Traverse column``        ``for` `(``int` `j = ``0``; j < N; j++)``        ``{``            ``System.out.print(M[i][j] + ``" "``);``        ``}``        ``System.out.println();``    ``}``}`` ` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``// Given size of matrix N``    ``int` `N = ``3``;`` ` `    ``// Function Call``    ``createMatrix(N);``}``}` `// This code is contributed by Ritik Bansal`

## Python3

 `# Python3 program for the above approach` `# Function to construct a N * N``# matrix based on the given condition``def` `createMatrix(N):``    ` `    ``# Matrix with given size``    ``M ``=` `[[``0``] ``*` `N ``for` `i ``in` `range``(N)]` `    ``# Counter to insert elements``    ``# from 1 to N * N``    ``count ``=` `1``    ` `    ``for` `i ``in` `range``(N):` `        ``# Check if it is first row``        ``# or odd row of the matrix``        ``if` `(i ``%` `2` `=``=` `0``):``            ``for` `j ``in` `range``(N):` `                ``# Insert elements from``                ``# left to right``                ``M[i][j] ``=` `count``                ``count ``+``=` `1` `        ``# Condition if it is second``        ``# row or even row``        ``else``:` `            ``# Insert elements from``            ``# right to left``            ``for` `j ``in` `range``(N ``-` `1``, ``-``1``, ``-``1``):``                ``M[i][j] ``=` `count``                ``count ``+``=` `1` `    ``# Print the matrix``    ``for` `i ``in` `range``(N):` `        ``# Traverse column``        ``for` `j ``in` `range``(N):``            ``print``(M[i][j], end ``=` `" "``)` `        ``print``()` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``# Given size of matrix N``    ``N ``=` `3` `    ``# Function call``    ``createMatrix(N)` `# This code is contributed by mohit kumar 29`

## C#

 `// C# program for``// the above approach``using` `System;``class` `GFG{`` ` `// Function to construct a N * N``// matrix based on the given condition``static` `void` `createMatrix(``int` `N)``{``  ``// Matrix with given sizM``  ``int``[,] M = ``new` `int``[N, N];` `  ``// Counter to insert elements``  ``// from 1 to N * N``  ``int` `count = 1;``  ``for` `(``int` `i = 0; i < N; i++)``  ``{``    ``// Check if it is first row``    ``// or odd row of the matrix``    ``if` `(i % 2 == 0)``    ``{` `      ``for` `(``int` `j = 0; j < N; j++)``      ``{``        ``M[i, j] = count;``        ``count++;``      ``}``    ``}``    ``else``    ``{``      ``// Insert elements from``      ``// right to left``      ``for``(``int` `j = N - 1; j >= 0; j--)``      ``{``        ``M[i, j] = count;``        ``count += 1;``      ``}``    ``}``  ``}` `  ``// Print the matrix``  ``for` `(``int` `i = 0; i < N; i++)``  ``{``    ``// Traverse column``    ``for` `(``int` `j = 0; j < N; j++)``    ``{``      ``Console.Write(M[i, j] + ``" "``);``    ``}``    ``Console.WriteLine();``  ``}``}`` ` `// Driver Code``public` `static` `void` `Main()``{``  ``// Given size of matrix N``  ``int` `N = 3;` `  ``// Function Call``  ``createMatrix(N);``}``}` `// This code is contributed by Chitranayal`

## Javascript

 ``
Output:
```1 2 3
6 5 4
7 8 9```

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

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