# Magical Pattern

Given an integer N as input, the task is to print the Magical Pattern as given below:

N . . 3 2 1 2 3 . . N
. . . . . . . . . . .
3 3 3 3 2 1 2 3 3 3 3
2 2 2 2 2 1 2 2 2 2 2
1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 1 2 2 2 2 2
3 3 3 3 2 1 2 3 3 3 3
. . . . . . . . . . .
N . . 3 2 1 2 3 . . N

Examples:

```Input: 3
Output:
3 2 1 2 3
2 2 1 2 2
1 1 1 1 1
2 2 1 2 2
3 2 1 2 3

Input: 4
Output:
4 3 2 1 2 3 4
3 3 2 1 2 3 3
2 2 2 1 2 2 2
1 1 1 1 1 1 1
2 2 2 1 2 2 2
3 3 2 1 2 3 3
4 3 2 1 2 3 4
```

Approach:

1. Consider an input N = 3, so the overlapping matrix will be of row = 5 and column = 5 (ie 2 * N – 1) with all the entries as zero.
2. Define three variables start = N, inc = 0 and dec = 2 * N – 1 for manipulation.
3. Run a loop till start becomes zero.
4. The row with inc or (dec – 1) or the column with inc or (dec – 1) is filled with the start value.

so at start=3
matrix will be
3 3 3 3 3
3 0 0 0 3
3 0 0 0 3
3 0 0 0 3
3 3 3 3 3

5. Decrement dec, start and increment the inc value.
6. Repeat the step3
7. The loop will stop as start=0 and the desired pattern is obtained

Below are the implementation of the above approach:

## C++

 `// C++ program to print the magical pattern ` ` `  `#include ` `using` `namespace` `std; ` ` `  `void` `overLapping(``int` `N, ``int` `matrix[100][100]) ` `{ ` ` `  `    ``int` `max, inc = 0, dec, start; ` ` `  `    ``// The size of matrix ` `    ``max = 2 * N - 1; ` ` `  `    ``// Fixing the range ` `    ``dec = max; ` ` `  `    ``// Overlapping value ` `    ``start = N; ` ` `  `    ``while` `(start != 0) { ` `        ``for` `(``int` `row = 0; row < max; row++) { ` `            ``for` `(``int` `col = 0; col < max; col++) { ` `                ``if` `(row == inc ` `                    ``|| row == dec - 1 ` `                    ``|| col == dec - 1 ` `                    ``|| col == inc) { ` ` `  `                    ``matrix[row][col] = start; ` `                ``} ` `            ``} ` `        ``} ` `        ``start--; ` `        ``inc++; ` `        ``dec--; ` `    ``} ` ` `  `    ``// return matrix; ` `} ` ` `  `void` `DisplayMatrix(``int` `matrix[][100], ``int` `max) ` `{ ` `    ``// To display the overlapping matrix ` `    ``for` `(``int` `row = 0; row < max; row++) { ` `        ``for` `(``int` `col = 0; col < max; col++) { ` `            ``cout <<``" "``<< matrix[row][col]; ` `        ``} ` `        ``cout << endl; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `N; ` ` `  `    ``// Get the value of N ` `    ``N = 3; ` ` `  `    ``// Declaring the overlapping matrix ` `    ``int` `matrix[100][100]; ` ` `  `    ``// Create the magical matrix ` `    ``overLapping(N, matrix); ` ` `  `    ``// Print the magical matrix ` `    ``DisplayMatrix(matrix, (2 * N - 1)); ` `} `

## C

 `// C program to print the magical pattern ` `#include ` ` `  `void` `overLapping(``int` `N, ``int` `matrix[100][100]) ` `{ ` ` `  `    ``int` `max, inc = 0, dec, start; ` ` `  `    ``// The size of matrix ` `    ``max = 2 * N - 1; ` ` `  `    ``// Fixing the range ` `    ``dec = max; ` ` `  `    ``// Overlapping value ` `    ``start = N; ` ` `  `    ``while` `(start != 0) { ` `        ``for` `(``int` `row = 0; row < max; row++) { ` `            ``for` `(``int` `col = 0; col < max; col++) { ` `                ``if` `(row == inc ` `                    ``|| row == dec - 1 ` `                    ``|| col == dec - 1 ` `                    ``|| col == inc) { ` ` `  `                    ``matrix[row][col] = start; ` `                ``} ` `            ``} ` `        ``} ` `        ``start--; ` `        ``inc++; ` `        ``dec--; ` `    ``} ` ` `  `    ``// return matrix; ` `} ` ` `  `void` `DisplayMatrix(``int` `matrix[][100], ``int` `max) ` `{ ` `    ``// To display the overlapping matrix ` `    ``for` `(``int` `row = 0; row < max; row++) { ` `        ``for` `(``int` `col = 0; col < max; col++) { ` `            ``printf``(``"%d "``, matrix[row][col]); ` `        ``} ` `        ``printf``(``"\n"``); ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `N = 3; ` ` `  `    ``// Declaring the overlapping matrix ` `    ``int` `matrix[100][100]; ` ` `  `    ``// Create the magical matrix ` `    ``overLapping(N, matrix); ` ` `  `    ``// Print the magical matrix ` `    ``DisplayMatrix(matrix, (2 * N - 1)); ` `} `

## Java

 `// Java program to print the magical pattern ` ` `  `class` `GFG { ` ` `  `    ``static` `void` `overLapping(``int` `N, ``int` `matrix[][]) { ` ` `  `        ``int` `max, inc = ``0``, dec, start; ` ` `  `        ``// The size of matrix  ` `        ``max = ``2` `* N - ``1``; ` ` `  `        ``// Fixing the range  ` `        ``dec = max; ` ` `  `        ``// Overlapping value  ` `        ``start = N; ` ` `  `        ``while` `(start != ``0``) { ` `            ``for` `(``int` `row = ``0``; row < max; row++) { ` `                ``for` `(``int` `col = ``0``; col < max; col++) { ` `                    ``if` `(row == inc ` `                            ``|| row == dec - ``1` `                            ``|| col == dec - ``1` `                            ``|| col == inc) { ` ` `  `                        ``matrix[row][col] = start; ` `                    ``} ` `                ``} ` `            ``} ` `            ``start--; ` `            ``inc++; ` `            ``dec--; ` `        ``} ` ` `  `        ``// return matrix;  ` `    ``} ` ` `  `    ``static` `void` `DisplayMatrix(``int` `matrix[][], ``int` `max) { ` `        ``// To display the overlapping matrix  ` `        ``for` `(``int` `row = ``0``; row < max; row++) { ` `            ``for` `(``int` `col = ``0``; col < max; col++) { ` `                ``System.out.printf(``"%d "``, matrix[row][col]); ` `            ``} ` `            ``System.out.printf(``"\n"``); ` `        ``} ` `    ``} ` ` `  `// Driver code  ` `    ``public` `static` `void` `main(String[] args) { ` `        ``int` `N = ``3``; ` ` `  `        ``// Declaring the overlapping matrix  ` `        ``int` `matrix[][] = ``new` `int``[``100``][``100``]; ` ` `  `        ``// Create the magical matrix  ` `        ``overLapping(N, matrix); ` ` `  `        ``// Print the magical matrix  ` `        ``DisplayMatrix(matrix, (``2` `* N - ``1``)); ` `    ``} ` `} ` ` `  `// This code is contributed by Rajput-JI  `

## Python3

 `# Python3 program to print the magical pattern ` ` `  `def` `overLapping(N, matrix): ` ` `  `    ``inc ``=` `0` ` `  `    ``# The size of matrix ` `    ``Max` `=` `2` `*` `N ``-` `1` ` `  `    ``# Fixing the range ` `    ``dec ``=` `Max` ` `  `    ``# Overlapping value ` `    ``start ``=` `N ` ` `  `    ``while` `(start !``=` `0``):  ` `        ``for` `row ``in` `range``(``Max``):  ` `            ``for` `col ``in` `range``(``Max``):  ` `                ``if` `(row ``=``=` `inc ``or` `row ``=``=` `dec ``-` `1` `or`  `                    ``col ``=``=` `dec ``-` `1` `or` `col ``=``=` `inc): ` `                    ``matrix[row][col] ``=` `start ` `             `  `        ``start ``-``=` `1` `        ``inc ``+``=` `1` `        ``dec ``-``=` `1` `     `  `    ``# return matrix ` ` `  `def` `DisplayMatrix(matrix, ``Max``): ` ` `  `    ``# To display the overlapping matrix ` `    ``for` `row ``in` `range``(``Max``):  ` `        ``for` `col ``in` `range``(``Max``): ` `            ``print``(matrix[row][col], end ``=` `" "``) ` `         `  `        ``print``() ` `     `  `# Driver code ` ` `  `# Get the value of N ` `N ``=` `3` ` `  `# Declaring the overlapping matrix ` `matrix ``=` `[[``0` `for` `i ``in` `range``(``100``)]  ` `             ``for` `i ``in` `range``(``100``)] ` ` `  `# Create the magical matrix ` `overLapping(N, matrix) ` ` `  `# Print the magical matrix ` `DisplayMatrix(matrix, (``2` `*` `N ``-` `1``)) ` ` `  `# This code is contributed by  ` `# Mohit Kumar 29 `

## C#

 `// C# program to print the magical pattern ` `using` `System;  ` ` `  `class` `GFG  ` `{  ` `public` `static` `void` `overLapping(``int` `N,  ` `                               ``int``[,] matrix)  ` `{  ` `    ``int` `max, inc = 0, dec, start;  ` `    ``max = 2 * N - 1;  ` `    ``dec = max;  ` `    ``start = N;  ` ` `  `    ``while` `(start != 0)  ` `    ``{  ` `        ``for` `(``int` `row = 0; row < max; row++) ` `        ``{  ` `            ``for` `(``int` `col = 0; col < max; col++) ` `            ``{  ` `                ``if` `(row == inc || row == dec - 1 || ` `                    ``col == dec - 1 || col == inc) ` `                ``{  ` `                    ``matrix[row, col] = start;  ` `                ``}  ` `            ``}  ` `        ``}  ` `        ``start--;  ` `        ``inc++;  ` `        ``dec--;  ` `    ``}  ` `}  ` ` `  `public` `static` `void` `DisplayMatrix(``int``[,] matrix, ``int` `max)  ` `{  ` `    ``for` `(``int` `row = 0; row < max; row++) ` `    ``{  ` `        ``for` `(``int` `col = 0; col < max; col++)  ` `        ``{  ` `            ``Console.Write(``" {0}"``, matrix[row, col]);  ` `        ``}  ` `        ``Console.Write(``"\n"``); ` `    ``}  ` `}  ` ` `  `// Driver Code ` `public` `static` `void` `Main()  ` `{  ` `    ``int` `N;  ` `    ``N = 3;  ` ` `  `    ``int``[,] matrix = ``new` `int``[100, 100];  ` ` `  `    ``overLapping(N, matrix);  ` `    ``DisplayMatrix(matrix, (2 * N - 1));  ` `}  ` `} ` ` `  `// This code is contributed by DrRoot_ `

## PHP

 ` `

Output:

```3 2 1 2 3
2 2 1 2 2
1 1 1 1 1
2 2 1 2 2
3 2 1 2 3
```

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