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# Print all palindromic paths from top left to bottom right in a matrix

• Difficulty Level : Medium
• Last Updated : 31 Aug, 2021

Given a matrix containing lower alphabetical characters only, we need to print all palindromic paths in given matrix. A path is defined as a sequence of cells starting from top-left cell and ending at bottom-right cell. We are allowed to move to right and down only from current cell. We cannot go down diagonally.
Example:

```Input : mat[][] = {"aaab”,
"baaa”
“abba”}
Output :aaaaaa, aaaaaa, abaaba

Explanation :
aaaaaa (0, 0) -> (0, 1) -> (1, 1) ->
(1, 2) -> (1, 3) -> (2, 3)
aaaaaa (0, 0) -> (0, 1) -> (0, 2) ->
(1, 2) -> (1, 3) -> (2, 3)
abaaba (0, 0) -> (1, 0) -> (1, 1) ->
(1, 2) -> (2, 2) -> (2, 3)```

Order of elements in the output array doesn’t matter.

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The idea is simple. We start from top left (0, 0) and explore all paths to bottom right. If a path turns to be palindrome, we print it.

## C++

 `// C++ program to print all palindromic paths``// from top left to bottom right in a grid.``#include``using` `namespace` `std;``#define N 4``bool` `isPalin(string str)``{``    ``int` `len = str.length() / 2;``    ``for` `(``int` `i = 0; i < len; i++)``    ``{``        ``if` `(str[i] != str[str.length() - i - 1])``            ``return` `false``;``    ``}``    ``return` `true``;``}` `// i and j are row and column indexes of current cell``// (initially these are 0 and 0).``void` `palindromicPath(string str, ``char` `a[][N],``                            ``int` `i, ``int` `j, ``int` `m, ``int` `n)``{``        ` `    ``// If we have not reached bottom right corner, keep``    ``// exploring``    ``if` `(j < m - 1 || i < n - 1)``    ``{``        ``if` `(i < n - 1)``            ``palindromicPath(str + a[i][j], a, i + 1, j, m, n);``        ``if` `(j < m - 1)``            ``palindromicPath(str + a[i][j], a, i, j + 1, m, n);``    ``}` `    ``// If we reach bottom right corner, we check if``    ``// if the path used is palindrome or not.``    ``else` `{``        ``str = str + a[n - 1][m - 1];``        ``if` `(isPalin(str))``            ``cout<<(str)<

## Java

 `// Java program to print all palindromic paths``// from top left to bottom right in a grid.``public` `class` `PalinPath {``    ``public` `static` `boolean` `isPalin(String str)``    ``{``        ``int` `len = str.length() / ``2``;``        ``for` `(``int` `i = ``0``; i < len; i++) {``            ``if` `(str.charAt(i) != str.charAt(str.length() - i - ``1``))``                ``return` `false``;``        ``}``        ``return` `true``;``    ``}` `    ``// i and j are row and column indexes of current cell``    ``// (initially these are 0 and 0).``    ``public` `static` `void` `palindromicPath(String str, ``char` `a[][],``                                 ``int` `i, ``int` `j, ``int` `m, ``int` `n)``    ``{``          ` `        ``// If we have not reached bottom right corner, keep``        ``// exploring``        ``if` `(j < m - ``1` `|| i < n - ``1``) {``          ``if` `(i < n - ``1``)``             ``palindromicPath(str + a[i][j], a, i + ``1``, j, m, n);``         ``if` `(j < m - ``1``)``             ``palindromicPath(str + a[i][j], a, i, j + ``1``, m, n);``        ``}` `        ``// If we reach bottom right corner, we check if``        ``// if the path used is palindrome or not.``        ``else` `{``            ``str = str + a[n - ``1``][m - ``1``];``            ``if` `(isPalin(str))``                ``System.out.println(str);``        ``}``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String args[])``    ``{``        ``char` `arr[][] = { { ``'a'``, ``'a'``, ``'a'``, ``'b'` `},``                         ``{ ``'b'``, ``'a'``, ``'a'``, ``'a'` `},``                         ``{ ``'a'``, ``'b'``, ``'b'``, ``'a'` `} };``        ``String str = ``""``;``        ``palindromicPath(str, arr, ``0``, ``0``, ``4``, ``3``);``    ``}``}`

## Python 3

 `# Python 3 program to print all``# palindromic paths from top left``# to bottom right in a grid.` `def` `isPalin(``str``):` `    ``l ``=` `len``(``str``) ``/``/` `2``    ``for` `i ``in` `range``( l) :``        ``if` `(``str``[i] !``=` `str``[``len``(``str``) ``-` `i ``-` `1``]):``            ``return` `False``        ` `    ``return` `True` `# i and j are row and column``# indexes of current cell``# (initially these are 0 and 0).``def` `palindromicPath(``str``, a, i, j, m, n):``        ` `    ``# If we have not reached bottom``    ``# right corner, keep exploring``    ``if` `(j < m ``-` `1` `or` `i < n ``-` `1``) :``        ``if` `(i < n ``-` `1``):``            ``palindromicPath(``str` `+` `a[i][j], a,``                            ``i ``+` `1``, j, m, n)``        ``if` `(j < m ``-` `1``):``            ``palindromicPath(``str` `+` `a[i][j], a,``                            ``i, j ``+` `1``, m, n)` `    ``# If we reach bottom right corner,``    ``# we check if the path used is``    ``# palindrome or not.``    ``else` `:``        ``str` `=` `str` `+` `a[n ``-` `1``][m ``-` `1``]``        ``if` `isPalin(``str``):``            ``print``(``str``)` `# Driver code``if` `__name__ ``=``=` `"__main__"``:``    ` `    ``arr ``=` `[[ ``'a'``, ``'a'``, ``'a'``, ``'b'` `],``           ``[``'b'``, ``'a'``, ``'a'``, ``'a'` `],``           ``[ ``'a'``, ``'b'``, ``'b'``, ``'a'` `]]``    ``str` `=` `""``    ``palindromicPath(``str``, arr, ``0``, ``0``, ``4``, ``3``)` `# This code is contributed``# by ChitraNayal`

## C#

 `// C# program to print all palindromic paths``// from top left to bottom right in a grid.``using` `System;` `class` `GFG``{``public` `static` `bool` `isPalin(``string` `str)``{``    ``int` `len = str.Length / 2;``    ``for` `(``int` `i = 0; i < len; i++)``    ``{``        ``if` `(str[i] != str[str.Length - i - 1])``        ``{``            ``return` `false``;``        ``}``    ``}``    ``return` `true``;``}` `// i and j are row and column indexes of``// current cell (initially these are 0 and 0).``public` `static` `void` `palindromicPath(``string` `str, ``char``[][] a,``                                   ``int` `i, ``int` `j, ``int` `m, ``int` `n)``{` `    ``// If we have not reached bottom``    ``// right corner, keep exploring``    ``if` `(j < m - 1 || i < n - 1)``    ``{``    ``if` `(i < n - 1)``    ``{``        ``palindromicPath(str + a[i][j],``                        ``a, i + 1, j, m, n);``    ``}``    ``if` `(j < m - 1)``    ``{``        ``palindromicPath(str + a[i][j],``                        ``a, i, j + 1, m, n);``    ``}``    ``}` `    ``// If we reach bottom right corner,``    ``// we check if the path used is``    ``// palindrome or not.``    ``else``    ``{``        ``str = str + a[n - 1][m - 1];``        ``if` `(isPalin(str))``        ``{``            ``Console.WriteLine(str);``        ``}``    ``}``}` `// Driver code``public` `static` `void` `Main(``string``[] args)``{``    ``char``[][] arr = ``new` `char``[][]``    ``{``        ``new` `char``[] {``'a'``, ``'a'``, ``'a'``, ``'b'``},``        ``new` `char``[] {``'b'``, ``'a'``, ``'a'``, ``'a'``},``        ``new` `char``[] {``'a'``, ``'b'``, ``'b'``, ``'a'``}``    ``};``    ``string` `str = ``""``;``    ``palindromicPath(str, arr, 0, 0, 4, 3);``}``}` `// This code is contributed by Shrikant13`

## Javascript

 ``

Output :

```abaaba
aaaaaa
aaaaaa```

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