Print all n digit patterns formed by mobile Keypad

Given a number n. we need to print all N digit pattern formed by mobile Keypad.
Note: we can move up, down, left, right from any key of mobile keypad and every pattern contain unique key.

Mobile-keypad

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 key as a starting digit for N_digit number one by one, after that we are try to generate all N digit pattern formed by this key( Using DFS because we can only move either up, left, right or down from that key).

 PrintPattern Function (DFS Function) 
  Add current key to pattern
  Pattern += Keypad[x][y]
 .... make current key as visited 
  visited[x][y] = true;
 ... Print pattern if size of Pattern == N 
 Call DFS for all 4 adjacent keypad key 
 __DFS_function
      

Below c++ implementation of above idea

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// C++ program to print all n digit patterns
// formed by mobile keypad.
#include <bits/stdc++.h>
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 vertice 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;
}

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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


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