 ### Generate all permutations of a string that follow given constraints

Given a string, generate all permutations of it that do not contain ‘B’ after ‘A’, i.e., the string should not contain “AB” as a substring.

Examples:

Input : str = “ABC”
Output : ACB, BAC, BCA, CBA
Out of 6 permutations of “ABC”, 4 follow the given constraint and 2 (“ABC” and “CAB”) do not follow.

Input : str = “BCD”
Output : BCD, BDC, CDB, CBD, DCB, DBC

A simple solution is to generate all permutations. For every permutation, check if it follows the given constraint.

 `#include ` `using` `namespace` `std; ` ` `  `void` `permute(string& str, ``int` `l, ``int` `r) ` `{ ` ` `  `    ` `    ` `    ``if` `(l == r) { ` `        ``if` `(str.find(``"AB"``) == string::npos) ` `            ``cout << str << ``" "``; ` `        ``return``; ` `    ``} ` ` `  `    ` `    ``for` `(``int` `i = l; i <= r; i++) { ` `        ``swap(str[l], str[i]); ` `        ``permute(str, l + 1, r); ` `        ``swap(str[l], str[i]); ` `    ``} ` `} ` ` `  `int` `main() ` `{ ` `    ``string str = ``"ABC"``; ` `    ``permute(str, 0, str.length() - 1); ` `    ``return` `0; ` `} `

The above solution first generates all permutations, then for every permutation it checks if it follows given constraint or not. An efficient solution is to use Backtracking. We cut down the recursion tree whenever we see that substring “AB” is formed. How do we do this? we add a isSafe() function. Before doing a swap, we check if previous character is ‘A’ and current character is ‘B’.

 `#include ` `using` `namespace` `std; ` ` `  `bool` `isSafe(string &str, ``int` `l, ``int` `i, ``int` `r) ` `{ ` `    ` `    ` `    ` `    ``if` `(l != 0 && str[l-1] == ``'A'` `&& str[i] == ``'B'``) ` `       ``return` `false``; ` ` `  `    ` `    ` `    ` `    ``if` `(r == l+1 && str[i] == ``'A'` `&& str[l] == ``'B'``) ` `      ``return` `false``; ` ` `  `   ``return` `true``; ` `} ` ` `  `void` `permute(string& str, ``int` `l, ``int` `r) ` `{ ` `    ` `    ` `    ``if` `(l == r) { ` `        ``cout << str << ``" "``; ` `        ``return``; ` `    ``} ` `     `  `    ` `    ``for` `(``int` `i = l; i <= r; i++) { ` ` `  `      ` `      ` `      ``if` `(isSafe(str, l, i, r)) { ` `        ``swap(str[l], str[i]); ` `        ``permute(str, l + 1, r); ` `        ``swap(str[l], str[i]); ` `      ``} ` `    ``} ` `} ` ` `  `int` `main() ` `{ ` `    ``string str = ``"ABC"``; ` `    ``permute(str, 0, str.length() - 1); ` `    ``return` `0; ` `} ` If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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