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Print all n digit patterns formed by mobile Keypad

Given a number n. we need to print all N digit patterns formed by mobile Keypad.

Note: we can move up, down, left, right from any key of mobile keypad, and every pattern contains the unique key.

Examples:

```
Input :   N = 3
Output :  all 3 digit Pattern are :
123, 125, 145, 147
236, 214, 258, 256, 254
321, 325, 369, 365
412, 456, 452, 458, 478
and so on ..```

idea of this solution is based on the DFS. We pick all keypad keys as a starting digit for N_digit number one by one, after that, we are trying to generate all N digit patterns formed by this key( Using DFS because we can only move either up, left, right, or down from that key).

``` PrintPattern Function (DFS Function)
.... make current key as visited
visited[x][y] = true;
... Print pattern if size of Pattern == N
__DFS_function```

Below is the implementation of the above idea :

C++

 `// C++ program to print all n digit patterns``// formed by mobile keypad.``#include ``using` `namespace` `std;` `// A function to check if a given cell (row, col)``// can be included in DFS``bool` `isSafe(``int` `x, ``int` `y, ``bool` `Visited[][3])``{``    ``// row number is in range, column number``    ``// is in range and not yet visited``    ``return` `(x >= 0 && x < 4 && y >= 0 &&``            ``y < 3 && !Visited[x][y]);``}` `// A utility function to do DFS for a mobile Keypad``// matrix. It only considers the 4 neighbors as``// adjacent vertices and print pattern of size n``void` `DFS(``bool` `visited[][3], ``int` `Keypad[][3], ``int` `n,``         ``string pattern, ``int` `x, ``int` `y)``{` `    ``// add current number to string``    ``pattern.push_back((Keypad[x][y] + ``'0'``));` `    ``// print pattern``    ``if` `(pattern.size() == n) {``        ``cout << pattern << ``" "``;``        ``return``;``    ``}` `    ``// These arrays are used to get row and``    ``// column``    ``// numbers of 4 neighbours of a given cell``    ``static` `int` `row[] = { 0, 1, 0, -1 };``    ``static` `int` `col[] = { 1, 0, -1, 0 };` `    ``// Mark this cell as visited``    ``visited[x][y] = ``true``;` `    ``// Recur for all connected neighbours``    ``for` `(``int` `k = 0; k < 4; k++)``        ``if` `(isSafe(x + row[k], y + col[k], visited)``            ``&& Keypad[x + row[k]][y + col[k]] != -1)``            ``DFS(visited, Keypad, n, pattern,``                       ``x + row[k], y + col[k]);` `    ``// unvisited``    ``visited[x][y] = ``false``;``    ``pattern.pop_back();``}` `void` `patternOfSizeK(``int` `Keypad[][3], ``int` `n)``{``    ``// Make a bool array to mark visited cells.``    ``// Initially all cells are unvisited``    ``bool` `visited[4][3];``    ``memset``(visited, ``false``, ``sizeof``(visited));` `    ``// try to generate all pattern of size n``    ``// by making every key of keypad as``    ``// starting char of pattern``    ``for` `(``int` `i = 0; i < 4; i++)``        ``for` `(``int` `j = 0; j < 3; j++)``            ``if` `(Keypad[i][j] != -1)``                ``DFS(visited, Keypad, n, ``""``, i, j);``}` `// Drive program to test above function.``int` `main()``{``    ``int` `Keypad[4][3] = { { 1, 2, 3 },``                         ``{ 4, 5, 6 },``                         ``{ 7, 8, 9 },``                         ``{ -1, 0, -1 } };``    ``int` `n = 3;``    ``patternOfSizeK(Keypad, n);``    ``return` `0;``}`

Java

 `// Java program to print all n digit patterns``// formed by mobile keypad.``public` `class` `Main``{``    ``// A function to check if a given cell (row, col)``    ``// can be included in DFS``    ``static` `boolean` `isSafe(``int` `x, ``int` `y, ``boolean``[][] Visited)``    ``{``      ` `        ``// row number is in range, column number``        ``// is in range and not yet visited``        ``return` `(x >= ``0` `&& x < ``4` `&& y >= ``0` `&&``                ``y < ``3` `&& !Visited[x][y]);``    ``}``      ` `    ``// A utility function to do DFS for a mobile Keypad``    ``// matrix. It only considers the 4 neighbors as``    ``// adjacent vertices and print pattern of size n``    ``static` `void` `DFS(``boolean``[][] visited, ``int``[][] Keypad, ``int` `n,``             ``String pattern, ``int` `x, ``int` `y)``    ``{``      ` `        ``// add current number to string``        ``pattern = pattern + Integer.toString(Keypad[x][y]);``      ` `        ``// print pattern``        ``if` `(pattern.length() == n) {``            ``System.out.print(pattern + ``" "``);``            ``return``;``        ``}``      ` `        ``// These arrays are used to get row and``        ``// column``        ``// numbers of 4 neighbours of a given cell``        ``int``[] row = { ``0``, ``1``, ``0``, -``1` `};``        ``int``[] col = { ``1``, ``0``, -``1``, ``0` `};``      ` `        ``// Mark this cell as visited``        ``visited[x][y] = ``true``;``      ` `        ``// Recur for all connected neighbours``        ``for` `(``int` `k = ``0``; k < ``4``; k++)``            ``if` `(isSafe(x + row[k], y + col[k], visited)``                ``&& Keypad[x + row[k]][y + col[k]] != -``1``)``                ``DFS(visited, Keypad, n, pattern,``                           ``x + row[k], y + col[k]);``      ` `        ``// unvisited``        ``visited[x][y] = ``false``;``        ``pattern = pattern.substring(``0``, pattern.length() - ``1``);``    ``}``      ` `    ``static` `void` `patternOfSizeK(``int``[][] Keypad, ``int` `n)``    ``{``      ` `        ``// Make a bool array to mark visited cells.``        ``// Initially all cells are unvisited``        ``boolean``[][] visited = ``new` `boolean``[``4``][``3``];``        ``for` `(``int` `i = ``0``; i < ``4``; i++)``        ``{``            ``for` `(``int` `j = ``0``; j < ``3``; j++)``            ``{``                ``visited[i][j] = ``false``;``            ``}``        ``}``      ` `        ``// try to generate all pattern of size n``        ``// by making every key of keypad as``        ``// starting char of pattern``        ``for` `(``int` `i = ``0``; i < ``4``; i++)``        ``{``            ``for` `(``int` `j = ``0``; j < ``3``; j++)``            ``{``                ``if` `(Keypad[i][j] != -``1``)``                    ``DFS(visited, Keypad, n, ``""``, i, j);``            ``}``        ``}``    ``}``    ` `  ``// Driver code``    ``public` `static` `void` `main(String[] args) {``        ``int``[][] Keypad = { { ``1``, ``2``, ``3` `},``                         ``{ ``4``, ``5``, ``6` `},``                         ``{ ``7``, ``8``, ``9` `},``                         ``{ -``1``, ``0``, -``1` `} };``        ``int` `n = ``3``;``        ``patternOfSizeK(Keypad, n);``    ``}``}` `// This code is contributed by divyesh072019.`

Python3

 `# Python3 program to print all n digit patterns``# formed by mobile keypad.`` ` `# A function to check if a given cell``# (row, col) can be included in DFS``def` `isSafe(x, y, Visited):` `    ``# row number is in range, column number``    ``# is in range and not yet visited``    ``return` `(x >``=` `0` `and` `x < ``4` `and``            ``y >``=` `0` `and` `y < ``3` `and` `not` `Visited[x][y])` `# A utility function to do DFS for a mobile Keypad``# matrix. It only considers the 4 neighbors as``# adjacent vertices and print pattern of size n``def` `DFS(visited, Keypad, n, pattern, x, y):``    ` `    ``# Add current number to string``    ``pattern ``=` `pattern ``+` `str``(Keypad[x][y])``    ` `    ``# Print pattern``    ``if` `(``len``(pattern) ``=``=` `n):``        ``print``(pattern, end ``=` `' '``)``        ``return``    ` `    ``# These arrays are used to get row and``    ``# column``    ``# numbers of 4 neighbours of a given cell``    ``row ``=` `[ ``0``, ``1``, ``0``, ``-``1` `]``    ``col ``=` `[ ``1``, ``0``, ``-``1``, ``0` `]`` ` `    ``# Mark this cell as visited``    ``visited[x][y] ``=` `True`` ` `    ``# Recur for all connected neighbours``    ``for` `k ``in` `range``(``0``, ``4``):``    ` `        ``if` `(isSafe(x ``+` `row[k],``                   ``y ``+` `col[k], visited) ``and``            ``Keypad[x ``+` `row[k]][y ``+` `col[k]] !``=` `-``1``):``            ``DFS(visited, Keypad, n, pattern,``                ``x ``+` `row[k], y ``+` `col[k])`` ` `    ``# unvisited``    ``visited[x][y] ``=` `False``;``    ``pattern ``=` `pattern[:``-``1``]` `def` `patternOfSizeK(Keypad, n):` `    ``# Make a bool array to mark visited cells.``    ``# Initially all cells are unvisited``    ``visited ``=` `[[``False` `for` `i ``in` `range``(``3``)]``                      ``for` `j ``in` `range``(``4``)]`` ` `    ``# Try to generate all pattern of size n``    ``# by making every key of keypad as``    ``# starting char of pattern``    ``for` `i ``in` `range``(``4``):``        ``for` `j ``in` `range``(``3``):``            ``if` `(Keypad[i][j] !``=` `-``1``):``                ``DFS(visited, Keypad, n,``                    ``"", i, j)` `# Driver code``if` `__name__``=``=``'__main__'``:` `    ``Keypad ``=` `[ [ ``1``, ``2``, ``3` `],``               ``[ ``4``, ``5``, ``6` `],``               ``[ ``7``, ``8``, ``9` `],``               ``[ ``-``1``, ``0``, ``-``1` `] ]``    ``n ``=` `3``    ` `    ``patternOfSizeK(Keypad, n)` `# This code is contributed by rutvik_56`

C#

 `// C# program to print all n digit patterns``// formed by mobile keypad.``using` `System;``class` `GFG {``    ` `    ``// A function to check if a given cell (row, col)``    ``// can be included in DFS``    ``static` `bool` `isSafe(``int` `x, ``int` `y, ``bool``[,] Visited)``    ``{``        ``// row number is in range, column number``        ``// is in range and not yet visited``        ``return` `(x >= 0 && x < 4 && y >= 0 &&``                ``y < 3 && !Visited[x,y]);``    ``}``     ` `    ``// A utility function to do DFS for a mobile Keypad``    ``// matrix. It only considers the 4 neighbors as``    ``// adjacent vertices and print pattern of size n``    ``static` `void` `DFS(``bool``[,] visited, ``int``[,] Keypad, ``int` `n,``             ``string` `pattern, ``int` `x, ``int` `y)``    ``{``     ` `        ``// add current number to string``        ``pattern = pattern + (Keypad[x,y]).ToString();``     ` `        ``// print pattern``        ``if` `(pattern.Length == n) {``            ``Console.Write(pattern + ``" "``);``            ``return``;``        ``}``     ` `        ``// These arrays are used to get row and``        ``// column``        ``// numbers of 4 neighbours of a given cell``        ``int``[] row = { 0, 1, 0, -1 };``        ``int``[] col = { 1, 0, -1, 0 };``     ` `        ``// Mark this cell as visited``        ``visited[x,y] = ``true``;``     ` `        ``// Recur for all connected neighbours``        ``for` `(``int` `k = 0; k < 4; k++)``            ``if` `(isSafe(x + row[k], y + col[k], visited)``                ``&& Keypad[x + row[k],y + col[k]] != -1)``                ``DFS(visited, Keypad, n, pattern,``                           ``x + row[k], y + col[k]);``     ` `        ``// unvisited``        ``visited[x,y] = ``false``;``        ``pattern = pattern.Substring(0, pattern.Length - 1);``    ``}``     ` `    ``static` `void` `patternOfSizeK(``int``[,] Keypad, ``int` `n)``    ``{``        ``// Make a bool array to mark visited cells.``        ``// Initially all cells are unvisited``        ``bool``[,] visited = ``new` `bool``[4,3];``        ``for` `(``int` `i = 0; i < 4; i++)``        ``{``            ``for` `(``int` `j = 0; j < 3; j++)``            ``{``                ``visited[i,j] = ``false``;``            ``}``        ``}``     ` `        ``// try to generate all pattern of size n``        ``// by making every key of keypad as``        ``// starting char of pattern``        ``for` `(``int` `i = 0; i < 4; i++)``        ``{``            ``for` `(``int` `j = 0; j < 3; j++)``            ``{``                ``if` `(Keypad[i,j] != -1)``                    ``DFS(visited, Keypad, n, ``""``, i, j);``            ``}``        ``}``    ``}` `  ``static` `void` `Main() {``    ``int``[,] Keypad = { { 1, 2, 3 },``                         ``{ 4, 5, 6 },``                         ``{ 7, 8, 9 },``                         ``{ -1, 0, -1 } };``    ``int` `n = 3;``    ``patternOfSizeK(Keypad, n);``  ``}``}` `// This code is contributed by suresh07.`

Javascript

 ``

Output

```123 125 145 147 236 256 258 254 214 369 365 325
321 456 458 452 478 412 569 563 589 580 587 547 541
523 521 698 658 654 652 632 789 780 785 745 741 896
874 856 854 852 980 987 985 965 963 089 087 085 ```

Time Complexity: O(4n)

Auxiliary Space: O(n), due to the DFS call stack.

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