# Rotate matrix by 45 degrees

Given a matrix mat[][] of size N*N, the task is to rotate the matrix by 45 degrees and print the matrix.

Examples:

Input: N = 6,
mat[][] = {{3, 4, 5, 1, 5, 9, 5},
{6, 9, 8, 7, 2, 5, 2},
{1, 5, 9, 7, 5, 3, 2},
{4, 7, 8, 9, 3, 5, 2},
{4, 5, 2, 9, 5, 6, 2},
{4, 5, 7, 2, 9, 8, 3}}
Output:
3
6 4
1 9 5
4 5 8 1
4 7 9 7 5
4 5 8 7 2 9
5 2 9 5 5
7 9 3 3
2 5 5
9 6
8

Input: N = 4,
mat[][] = {{2, 5, 7, 2},
{9, 1, 4, 3},
{5, 8, 2, 3},
{6, 4, 6, 3}}

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

Approach: Follow the steps given below in order to solve the problem:

1. Store the diagonal elements in a list using a counter variable.
2. Print the number of spaces required to make the output look like the desired pattern.
3. Print the list elements after reversing the list.
4. Traverse through only diagonal elements to optimize the time taken by the operation.

Below is the implementation of the above approach:

 `// C++ program for the above approach ` `#include ` `using` `namespace` `std;`   `// Function to rotate matrix by 45 degree` `void` `matrix(``int` `n, ``int` `m, vector> li)` `{` `    `  `    ``// Counter Variable ` `    ``int` `ctr = 0;` `    `  `    ``while` `(ctr < 2 * n - 1)` `    ``{` `        ``for``(``int` `i = 0; ` `                ``i < ``abs``(n - ctr - 1);` `                ``i++)` `        ``{` `            ``cout << ``" "``;` `        ``}` `        `  `        ``vector<``int``> lst;`   `        ``// Iterate [0, m] ` `        ``for``(``int` `i = 0; i < m; i++)` `        ``{` `            `  `            ``// Iterate [0, n] ` `            ``for``(``int` `j = 0; j < n; j++)` `            ``{` `                `  `                ``// Diagonal Elements ` `                ``// Condition ` `                ``if` `(i + j == ctr)` `                ``{` `                    `  `                    ``// Appending the ` `                    ``// Diagonal Elements ` `                    ``lst.push_back(li[i][j]);` `                ``}` `            ``}` `        ``}` `            `  `        ``// Printing reversed Diagonal ` `        ``// Elements ` `        ``for``(``int` `i = lst.size() - 1; i >= 0; i--)` `        ``{` `            ``cout << lst[i] << ``" "``;` `        ``}` `        ``cout << endl;` `        ``ctr += 1;` `    ``}` `}`   `// Driver code    ` `int` `main()` `{` `    `  `    ``// Dimensions of Matrix ` `    ``int` `n = 8;` `    ``int` `m = n; ` `    `  `    ``// Given matrix ` `    ``vector> li{ ` `        ``{ 4, 5, 6, 9, 8, 7, 1, 4 }, ` `        ``{ 1, 5, 9, 7, 5, 3, 1, 6 }, ` `        ``{ 7, 5, 3, 1, 5, 9, 8, 0 }, ` `        ``{ 6, 5, 4, 7, 8, 9, 3, 7 }, ` `        ``{ 3, 5, 6, 4, 8, 9, 2, 1 }, ` `        ``{ 3, 1, 6, 4, 7, 9, 5, 0 }, ` `        ``{ 8, 0, 7, 2, 3, 1, 0, 8 }, ` `        ``{ 7, 5, 3, 1, 5, 9, 8, 5 } };` `    `  `    ``// Function call ` `    ``matrix(n, m, li);`   `    ``return` `0;` `}`   `// This code is contributed by divyeshrabadiya07`

 `// Java program for ` `// the above approach ` `import` `java.util.*;` `class` `GFG{`   `// Function to rotate ` `// matrix by 45 degree` `static` `void` `matrix(``int` `n, ``int` `m, ` `                   ``int` `[][]li)` `{` `  ``// Counter Variable ` `  ``int` `ctr = ``0``;`   `  ``while` `(ctr < ``2` `* n - ``1``)` `  ``{` `    ``for``(``int` `i = ``0``; i < Math.abs(n - ctr - ``1``);` `            ``i++)` `    ``{` `      ``System.out.print(``" "``);` `    ``}`   `    ``Vector lst = ``new` `Vector();`   `    ``// Iterate [0, m] ` `    ``for``(``int` `i = ``0``; i < m; i++)` `    ``{` `      ``// Iterate [0, n] ` `      ``for``(``int` `j = ``0``; j < n; j++)` `      ``{` `        ``// Diagonal Elements ` `        ``// Condition ` `        ``if` `(i + j == ctr)` `        ``{` `          ``// Appending the ` `          ``// Diagonal Elements ` `          ``lst.add(li[i][j]);` `        ``}` `      ``}` `    ``}`   `    ``// Printing reversed Diagonal ` `    ``// Elements ` `    ``for``(``int` `i = lst.size() - ``1``; i >= ``0``; i--)` `    ``{` `      ``System.out.print(lst.get(i) + ``" "``);` `    ``}` `    `  `    ``System.out.println();` `    ``ctr += ``1``;` `  ``}` `}`   `// Driver code    ` `public` `static` `void` `main(String[] args)` `{    ` `  ``// Dimensions of Matrix ` `  ``int` `n = ``8``;` `  ``int` `m = n; `   `  ``// Given matrix ` `  ``int``[][] li = {{``4``, ``5``, ``6``, ``9``, ``8``, ``7``, ``1``, ``4``}, ` `                ``{``1``, ``5``, ``9``, ``7``, ``5``, ``3``, ``1``, ``6``}, ` `                ``{``7``, ``5``, ``3``, ``1``, ``5``, ``9``, ``8``, ``0``}, ` `                ``{``6``, ``5``, ``4``, ``7``, ``8``, ``9``, ``3``, ``7``}, ` `                ``{``3``, ``5``, ``6``, ``4``, ``8``, ``9``, ``2``, ``1``}, ` `                ``{``3``, ``1``, ``6``, ``4``, ``7``, ``9``, ``5``, ``0``}, ` `                ``{``8``, ``0``, ``7``, ``2``, ``3``, ``1``, ``0``, ``8``}, ` `                ``{``7``, ``5``, ``3``, ``1``, ``5``, ``9``, ``8``, ``5``}};`   `  ``// Function call ` `  ``matrix(n, m, li);` `}` `}`   `// This code is contributed by Princi Singh`

 `# Python3 program for the above approach`   `# Function to rotate matrix by 45 degree`     `def` `matrix(n, m, li):`   `    ``# Counter Variable` `    ``ctr ``=` `0` `    ``while``(ctr < ``2` `*` `n``-``1``):` `        ``print``(``" "``*``abs``(n``-``ctr``-``1``), end ``=``"")` `        ``lst ``=` `[]`   `        ``# Iterate [0, m]` `        ``for` `i ``in` `range``(m):`   `                ``# Iterate [0, n]` `            ``for` `j ``in` `range``(n):`   `                ``# Diagonal Elements` `                ``# Condition` `                ``if` `i ``+` `j ``=``=` `ctr:`   `                    ``# Appending the` `                    ``# Diagonal Elements` `                    ``lst.append(li[i][j])`   `        ``# Printing reversed Diagonal` `        ``# Elements` `        ``lst.reverse()` `        ``print``(``*``lst)` `        ``ctr ``+``=` `1`     `# Driver Code`   `# Dimensions of Matrix` `n ``=` `8` `m ``=` `n`   `# Given matrix` `li ``=` `[[``4``, ``5``, ``6``, ``9``, ``8``, ``7``, ``1``, ``4``],` `      ``[``1``, ``5``, ``9``, ``7``, ``5``, ``3``, ``1``, ``6``],` `      ``[``7``, ``5``, ``3``, ``1``, ``5``, ``9``, ``8``, ``0``],` `      ``[``6``, ``5``, ``4``, ``7``, ``8``, ``9``, ``3``, ``7``],` `      ``[``3``, ``5``, ``6``, ``4``, ``8``, ``9``, ``2``, ``1``],` `      ``[``3``, ``1``, ``6``, ``4``, ``7``, ``9``, ``5``, ``0``],` `      ``[``8``, ``0``, ``7``, ``2``, ``3``, ``1``, ``0``, ``8``],` `      ``[``7``, ``5``, ``3``, ``1``, ``5``, ``9``, ``8``, ``5``]]`   `# Function Call` `matrix(n, m, li)`

 `// C# program for ` `// the above approach ` `using` `System;` `using` `System.Collections;` `class` `GFG{` ` `  `// Function to rotate ` `// matrix by 45 degree` `static` `void` `matrix(``int` `n, ``int` `m, ` `                   ``int` `[,]li)` `{` `  ``// Counter Variable ` `  ``int` `ctr = 0;`   `  ``while` `(ctr < 2 * n - 1)` `  ``{` `    ``for``(``int` `i = 0; ` `            ``i < Math.Abs(n - ctr - 1);` `            ``i++)` `    ``{` `      ``Console.Write(``" "``);` `    ``}`   `    ``ArrayList lst = ``new` `ArrayList();`   `    ``// Iterate [0, m] ` `    ``for``(``int` `i = 0; i < m; i++)` `    ``{` `      ``// Iterate [0, n] ` `      ``for``(``int` `j = 0; j < n; j++)` `      ``{` `        ``// Diagonal Elements ` `        ``// Condition ` `        ``if` `(i + j == ctr)` `        ``{` `          ``// Appending the ` `          ``// Diagonal Elements ` `          ``lst.Add(li[i, j]);` `        ``}` `      ``}` `    ``}`   `    ``// Printing reversed Diagonal ` `    ``// Elements ` `    ``for``(``int` `i = lst.Count - 1; ` `            ``i >= 0; i--)` `    ``{` `      ``Console.Write((``int``)lst[i] + ``" "``);` `    ``}`   `    ``Console.Write(``"\n"``);` `    ``ctr += 1;` `  ``}` `}` ` `  `// Driver code    ` `public` `static` `void` `Main(``string``[] args)` `{    ` `  ``// Dimensions of Matrix ` `  ``int` `n = 8;` `  ``int` `m = n; ` ` `  `  ``// Given matrix ` `  ``int``[,] li = {{4, 5, 6, 9, 8, 7, 1, 4}, ` `               ``{1, 5, 9, 7, 5, 3, 1, 6}, ` `               ``{7, 5, 3, 1, 5, 9, 8, 0}, ` `               ``{6, 5, 4, 7, 8, 9, 3, 7}, ` `               ``{3, 5, 6, 4, 8, 9, 2, 1}, ` `               ``{3, 1, 6, 4, 7, 9, 5, 0}, ` `               ``{8, 0, 7, 2, 3, 1, 0, 8}, ` `               ``{7, 5, 3, 1, 5, 9, 8, 5}};` ` `  `  ``// Function call ` `  ``matrix(n, m, li);` `}` `}`   `// This code is contributed by Rutvik_56`

Output:
```       4
1 5
7 5 6
6 5 9 9
3 5 3 7 8
3 5 4 1 5 7
8 1 6 7 5 3 1
7 0 6 4 8 9 1 4
5 7 4 8 9 8 6
3 2 7 9 3 0
1 3 9 2 7
5 1 5 1
9 0 0
8 8
5

```

Time Complexity: O(N2)
Auxiliary Space: O(1)

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