Given a string S of length N consisting of lowercase English letters and an integer K. Find the lexicographically smallest string T of length K, such that its set of letters is a subset of the set of letters of S and T is lexicographically greater than S. Note: The set of letters is a set, not a multiset. For example, the set of letters of abadaba is {a, b, d}.
Examples:
Input : S = “abc”, K = 3
Output : T = “aca”
Explanation: The list of strings T of length 3, such that the set of letters of T is a subset of letters of S is as follows: “aaa”, “aab”, “aac”, “aba”, “abb”, “abc”, “aca”, “acb”, …. Among them, those which are lexicographically greater than “abc”:
“aca”, “acb”, …. Out of those the lexicographically smallest is “aca”.Input : S = “abc”, K = 2
Output : T = “ac”
A simple solution is to one by on try all strings of length k in increasing order. For every string, check if it is greater than S, if yes, then return it.
Below is an efficient method to solve this problem.
Let’s consider two cases:
1. If N < K: For this case, we can simply copy the string S to string T for upto N characters and for the remaining (K – N) characters we can append the minimum character (least ASCII value) in string S to string T (K – N) times since we have to find the lexicographically smallest string which is just greater than string S.
2. If N ? K: For this case, we need to copy the string S to string T for upto K characters and then for string T by iterating in reverse direction we have to replace all those characters by some character until the string T becomes the lexicographically smallest string greater than string S. For this we can do the following:
- Store the characters of string S in a STL set (ofcourse, in sorted order)
- Copy the string S to string T upto K characters.
- Iterating in reverse direction, find a character (let it be found at position ‘p’) for which there exists some character having greater ASCII value in the set.
- Replace this character with that found in the set.
- Replace all characters with minimum character after (p + 1)th index upto Kth index.
Illustration: Let S = “bcegikmyyy”, N = 10, K = 9. Set = { b, c, e, g, i, k, m, y }. Copy string S to T upto K characters T = “bcegikmyy”. Then iterating in reverse direction, we first have ‘y’ but there is no greater character than ‘y’ in the set so move ahead. Again we have ‘y’, move ahead now we have ‘m’ for which there is a greater character ‘y’ in the set. Replace ‘m’ with ‘y’ and then after ‘m’ in forward direction replace all characters with minimum character i.e. ‘b’. Hence the string T becomes T = “bcegikybb”;
CPP
/* CPP Program to find the lexicographically smallest string T greater than S whose letters are subset of letters of S */ #include <bits/stdc++.h> using namespace std; // function to find the lexicographically // smallest string greater than S string findString(string S, int N, int K) { // stores minimum character char minChar = 'z' ; // stores unique characters of // string in sorted order set< char > found; // Loop through to find the minimum character // and stores characters in the set for ( int i = 0; i < N; i++) { found.insert(S[i]); if (S[i] < minChar) minChar = S[i]; } string T; // Case 1: If N < K if (N < K) { // copy the string S upto N characters T = S; // append minChar to make the remaining // characters for ( int i = 0; i < (K - N); i++) T += minChar; } // Case 2 : If N >= K else { T = "" ; // copy the string S upto K characters for ( int i = 0; i < K; i++) T += S[i]; int i; // an iterator to the set set< char >::iterator it; // iterating in reverse direction for (i = K - 1; i >= 0; i--) { // find the current character in the set it = found.find(T[i]); // increment the iterator it++; // check if some bigger character exists in set if (it != found.end()) break ; } // Replace current character with that found in set T[i] = *it; // Replace all characters after with minChar for ( int j = i + 1; j < K; j++) T[j] = minChar; } return T; } // Driver Code to test the above function int main() { string S = "abc" ; int N = S.length(); // Length of required string int K = 3; string T = findString(S, N, K); cout << "Lexicographically Smallest String " "greater than " << S << " is " << T << endl; return 0; } |
Java
import java.util.*; public class LexicographicallySmallest { // function to find the lexicographically // smallest string greater than S public static String findString(String S, int N, int K) { // stores minimum character char minChar = 'z' ; // stores unique characters of // string in sorted order Set<Character> found = new HashSet<>(); // Loop through to find the minimum character // and stores characters in the set for ( int i = 0 ; i < N; i++) { found.add(S.charAt(i)); if (S.charAt(i) < minChar) { minChar = S.charAt(i); } } StringBuilder T = new StringBuilder(); // Case 1: If N < K if (N < K) { // copy the string S upto N characters T.append(S); // append minChar to make the remaining // characters for ( int i = 0 ; i < K - N; i++) { T.append(minChar); } } // Case 2 : If N >= K else { T = new StringBuilder(); // copy the string S upto K characters for ( int i = 0 ; i < K; i++) { T.append(S.charAt(i)); } // iterating in reverse direction int i; for (i = K - 1 ; i >= 0 ; i--) { // find the current character in the set if (found.contains(T.charAt(i))) { char it = T.charAt(i); // increment the iterator it = ( char )(it + 1 ); // check if some bigger character exists in set if (found.contains(it)) { break ; } } } // Replace current character with that found in set char [] charArray = T.toString().toCharArray(); charArray[i] = ( char )(charArray[i] + 1 ); T = new StringBuilder(String.valueOf(charArray)); // Replace all characters after with minChar for ( int j = i + 1 ; j < K; j++) { T.setCharAt(j, minChar); } } return T.toString(); } // Driver Code to test the above function public static void main(String[] args) { String S = "abc" ; int N = S.length(); // Length of required string int K = 3 ; String T = findString(S, N, K); System.out.println( "Lexicographically Smallest String greater than " + S + " is " + T); } } |
Python3
''' Python 3 Program to find the lexicographically smallest string T greater than S whose letters are subset of letters of S ''' # function to find the lexicographically # smallest string greater than S def findString(S, N, K): # stores minimum character minChar = 'z' # stores unique characters of # string in sorted order found = set ([]) # Loop through to find the minimum character # and stores characters in the set for i in range (N): found.add(S[i]) if (S[i] < minChar): minChar = S[i] T = "" # Case 1: If N < K if (N < K): # copy the string S upto N characters T = S # append minChar to make the remaining # characters for i in range ((K - N)): T + = minChar # Case 2 : If N >= K else : T = "" # copy the string S upto K characters for i in range (K): T + = S[i] T = list (T) # iterating in reverse direction for i in range (K - 1 , - 1 , - 1 ): # find the current character in the set if (T[i] in found): it = T[i] # increment the iterator it = chr ( ord (it) + 1 ) # check if some bigger character exists in set if (it in found): break # Replace current character with that found in set T[i] = it # Replace all characters after with minChar for j in range (i + 1 , K): T[j] = minChar return T # Driver Code to test the above function if __name__ = = "__main__" : S = "abc" N = len (S) # Length of required string K = 3 T = findString(S, N, K) print ( "Lexicographically Smallest String " "greater than " + S + " is " + "".join(T)) # This code s contributed by ukasp. |
C#
/* C# Program to find the lexicographically smallest string T greater than S whose letters are subset of letters of S */ using System; using System.Collections.Generic; public class LexicographicallySmallest { // function to find the lexicographically // smallest string greater than S public static string FindString( string S, int N, int K) { // stores minimum character char minChar = 'z' ; // stores unique characters of // string in sorted order HashSet < char > found = new HashSet < char > (); // Loop through to find the minimum character // and stores characters in the set for ( int i = 0; i < N; i++) { found.Add(S[i]); if (S[i] < minChar) { minChar = S[i]; } } string T = "" ; // Case 1: If N < K if (N < K) { // copy the string S upto N characters T += S; // append minChar to make the remaining // characters for ( int i = 0; i < K - N; i++) { T += minChar; } } // Case 2 : If N >= K else { T = "" ; // copy the string S upto K characters for ( int i = 0; i < K; i++) { T += S[i]; } // iterating in reverse direction int j; for (j = K - 1; j >= 0; j--) { // find the current character in the set if (found.Contains(T[j])) { char it = T[j]; // increment the iterator it = ( char )(it + 1); // check if some bigger character exists in set if (found.Contains(it)) { break ; } } } // Replace current character with that found in set char [] charArray = T.ToCharArray(); charArray[j] = ( char )(charArray[j] + 1); T = new string (charArray); // Replace all characters after with minChar for ( int k = j + 1; k < K; k++) { charArray[k] = minChar; } T = new string (charArray); } return T; } // Driver Code to test the above function public static void Main( string [] args) { string S = "abc" ; int N = S.Length; // Length of required string int K = 3; string T = FindString(S, N, K); Console.WriteLine( "Lexicographically Smallest String greater than " + S + " is " + T); } } // Contributed by adityasharmadev01 |
Javascript
// function to find the lexicographically // smallest string greater than S function findString(S, N, K) { // stores minimum character let minChar = "z" ; // stores unique characters of // string in sorted order let found = new Set(); // Loop through to find the minimum character // and stores characters in the set for (let i = 0; i < N; i++) { found.add(S[i]); if (S[i] < minChar) { minChar = S[i]; } } let T = "" ; // Case 1: If N < K if (N < K) { // copy the string S upto N characters T = S; // append minChar to make the remaining // characters for (let i = 0; i < K - N; i++) { T += minChar; } } // Case 2 : If N >= K else { T = "" ; // copy the string S upto K characters for (let i = 0; i < K; i++) { T += S[i]; } T = T.split( "" ); // iterating in reverse direction let i; for (i = K - 1; i >= 0; i--) { // find the current character in the set if (found.has(T[i])) { var it = T[i]; } // increment the iterator it = String.fromCharCode(it.charCodeAt(0) + 1); // check if some bigger character exists in set if (found.has(it)) { break ; } } // Replace current character with that found in set T[i] = it; // Replace all characters after with minChar for (let j = i + 1; j < K; j++) { T[j] = minChar; } } return T.join( "" ); } // Driver Code to test the above function let S = "abc" ; let N = S.length; // Length of required string let K = 3; let T = findString(S, N, K); console.log( "Lexicographically Smallest String greater than " + S + " is " + T ); // This code is contributed by codebraxnzt |
Lexicographically Smallest String greater than abc is aca
Time Complexity: O(N + K), where N is the length of given string and K is the length of required string.
Space Complexity : O(K)
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