Power Set in Lexicographic order
This article is about generating Power set in lexicographical order.
Examples :
Input : abc Output : a ab abc ac b bc c
The idea is to sort array first. After sorting, one by one fix characters and recursively generates all subsets starting from them. After every recursive call, we remove last character so that next permutation can be generated.
C++
// CPP program to generate power set in // lexicographic order. #include <bits/stdc++.h> using namespace std; // str : Stores input string // n : Length of str. // curr : Stores current permutation // index : Index in current permutation, curr void permuteRec(string str, int n, int index = -1, string curr = "") { // base case if (index == n) return; cout << curr << "\n"; for (int i = index + 1; i < n; i++) { curr += str[i]; permuteRec(str, n, i, curr); // backtracking curr = curr.erase(curr.size() - 1); } return; } // Generates power set in lexicographic // order. void powerSet(string str) { sort(str.begin(), str.end()); permuteRec(str, str.size()); } // Driver code int main() { string str = "cab"; powerSet(str); return 0; } |
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Java
// Java program to generate power set in // lexicographic order. import java.util.*; class GFG { // str : Stores input string // n : Length of str. // curr : Stores current permutation // index : Index in current permutation, curr static void permuteRec(String str, int n, int index, String curr) { // base case if (index == n) { return; } System.out.println(curr); for (int i = index + 1; i < n; i++) { curr += str.charAt(i); permuteRec(str, n, i, curr); // backtracking curr = curr.substring(0, curr.length() - 1); } return; } // Generates power set in lexicographic // order. static void powerSet(String str) { char[] arr = str.toCharArray(); Arrays.sort(arr); permuteRec(new String(arr), str.length(), -1, ""); } // Driver code public static void main(String[] args) { String str = "cab"; powerSet(str); } } /* This code contributed by PrinciRaj1992 */ |
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Python3
# Python3 program to generate power # set in lexicographic order. # str : Stores input string # n : Length of str. # curr : Stores current permutation # index : Index in current permutation, curr def permuteRec(string, n, index = -1, curr = ""): # base case if index == n: return if len(curr) > 0: print(curr) for i in range(index + 1, n): curr += string[i] permuteRec(string, n, i, curr) # backtracking curr = curr[:len(curr) - 1] # Generates power set in lexicographic order def powerSet(string): string = ''.join(sorted(string)) permuteRec(string, len(string)) # Driver Code if __name__ == "__main__": string = "cab" powerSet(string) # This code is contributed by vibhu4agarwal |
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C#
// C# program to generate power set in // lexicographic order. using System; class GFG { // str : Stores input string // n : Length of str. // curr : Stores current permutation // index : Index in current permutation, curr static void permuteRec(String str, int n, int index, String curr) { // base case if (index == n) { return; } Console.WriteLine(curr); for (int i = index + 1; i < n; i++) { curr += str[i]; permuteRec(str, n, i, curr); // backtracking curr = curr.Substring(0, curr.Length - 1); } return; } // Generates power set in lexicographic // order. static void powerSet(String str) { char[] arr = str.ToCharArray(); Array.Sort(arr); permuteRec(new String(arr), str.Length, -1, ""); } // Driver code public static void Main(String[] args) { String str = "cab"; powerSet(str); } } // This code contributed by Rajput-Ji |
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PHP
<?php // PHP program to generate power // set in lexicographic order. // str : Stores input string // n : Length of str. // curr : Stores current permutation // index : Index in current permutation, curr function permuteRec($str, $n, $index = -1, $curr = "") { // base case if ($index == $n) return; echo $curr."\n"; for ($i = $index + 1; $i < $n; $i++) { $curr=$curr.$str[$i]; permuteRec($str, $n, $i, $curr); // backtracking $curr =""; } return; } // Generates power set in lexicographic // order. function powerSet($str) { $str = str_split($str); sort($str); permuteRec($str, sizeof($str)); } // Driver code $str = "cab"; powerSet($str); // This code is contributed by Mithun Kumar ?> |
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Output :
a ab abc ac b bc c
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