# Generating distinct subsequences of a given string in lexicographic order

Last Updated : 10 Mar, 2023

Given a string s, make a list of all possible combinations of letters of a given string S. If there are two strings with the same set of characters, print the lexicographically smallest arrangement of the two strings
For string abc, the list in lexicographic order subsequences are, a ab abc ac b bc c

Examples:

```Input : s = "ab"
Output : a ab b

Input  : xyzx
Output : x xx xy xyx xyz xyzx xz xzx y
yx yz yzx z zx```

The idea is to use a set (which is implemented using self balancing BST) to store subsequences so that duplicates can be tested.
To generate all subsequences, we one by one remove every character and recur for remaining string.

Implementation:

## Python 3

 `# Python program to print all distinct ` `# subsequences of a string.`   `# Finds and stores result in st for a given` `# string s.` `def` `generate(st, s):` `    ``if` `len``(s) ``=``=` `0``:` `        ``return`   `    ``# If current string is not already present.` `    ``if` `s ``not` `in` `st:` `        ``st.add(s)`   `        ``# Traverse current string, one by one` `        ``# remove every character and recur.` `        ``for` `i ``in` `range``(``len``(s)):` `            ``t ``=` `list``(s).copy()` `            ``t.remove(s[i])` `            ``t ``=` `''.join(t)` `            ``generate(st, t)`   `    ``return`     `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:` `    ``s ``=` `"xyz"` `    ``st ``=` `set``()` `    ``generate(st, s)` `    ``for` `i ``in` `st:` `        ``print``(i)`   `# This code is contributed by` `# sanjeev2552`

## C#

 `// C# program to print all distinct subsequences` `// of a string.` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG {`   `    ``// Finds and stores result in st for a given` `    ``// string s.` `    ``static` `void` `generate(HashSet st, String s)` `    ``{` `        ``if` `(s.Length == 0) {` `            ``return``;` `        ``}`   `        ``// If current string is not already present.` `        ``if` `(!st.Contains(s)) {` `            ``st.Add(s);`   `            ``// Traverse current string, one by one` `            ``// remove every character and recur.` `            ``for` `(``int` `i = 0; i < s.Length; i++) {` `                ``String t = s;` `                ``t = t.Substring(0, i) + t.Substring(i + 1);` `                ``generate(st, t);` `            ``}` `        ``}` `        ``return``;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``String s = ``"xyz"``;` `        ``HashSet st = ``new` `HashSet();` `        ``generate(st, s);` `        ``foreach``(String str ``in` `st)` `        ``{` `            ``Console.WriteLine(str);` `        ``}` `    ``}` `}`   `/* This code contributed by PrinciRaj1992 */`

## Javascript

 ``

Output

```x
xy
xyz
xz
y
yz
z```

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

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