Minimum size lexicographically smallest string which is not a substring of given string
Last Updated :
15 Dec, 2021
Given a string s, the task is to find the lexicographically smallest string of minimum characters that do not exist as a substring in S.
Examples:
Input: S = "aabacdefghijklmnopqrstuvwxyz"
Output: ad
Explanation: All the single digit strings from [a-z] occur in the given string and in two character strings, strings {aa, ab, ac} occur but "ad" is not present in the given string.
Input: S = "geeksforgeeks"
Output: a
Input: S = "abcd"
Output: e
Approach: The problem can be solved using BFS (Breadth-First Search) algorithm. Generate all strings in lexicographical order and check if it exists as a substring in the given string or not. Follow the steps below to solve the problem:
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find the lexicographically
// smallest string of minimum characters
// not present as substring in string S
void lexicographicalSmallestString(string& S, int n)
{
// Set which stores all substrings
// of the string S
set<string> collection;
// Constructing all substrings of S
for (int i = 0; i < n; ++i) {
string cur;
for (int j = i; j < n; ++j) {
cur.push_back(S[j]);
// Inserting the current
// substring to set
collection.insert(cur);
}
}
queue<string> q;
// Initializing BFS queue
for (int i = 0; i < 26; ++i) {
q.push(string(1, i + 'a'));
}
// Loop for the BFS Traversal
while (!q.empty()) {
// Stores the current
// lexicographically smallest
// string of min characters
auto cur = q.front();
q.pop();
// If the current string is
// not present as a substring
// of the given string
if (collection.find(cur) == collection.end()) {
// Print Answer
cout << cur << endl;
return;
}
// Append characters from [a-z]
// to the back of string cur
// and push into the queue.
for (int i = 0; i < 26; ++i) {
cur.push_back(i + 'a');
q.push(cur);
cur.pop_back();
}
}
}
// Driver Code
int main()
{
string S = "aabacdefghijklmnopqrstuvwxyz";
int N = S.length();
lexicographicalSmallestString(S, N);
}
// Java implementation of the above approach
import java.util.*;
class GFG{
// Function to find the lexicographically
// smallest String of minimum characters
// not present as subString in String S
static void lexicographicalSmallestString(char[] S, int n)
{
// Set which stores all subStrings
// of the String S
HashSet<String> collection = new HashSet<String>();
// Constructing all subStrings of S
for (int i = 0; i < n; ++i) {
String cur="";
for (int j = i; j < n; ++j) {
cur+=(S[j]);
// Inserting the current
// subString to set
collection.add(cur);
}
}
Queue<String> q = new LinkedList<String>();
// Initializing BFS queue
for (int i = 0; i < 26; ++i) {
q.add(String.valueOf((char)((i + 'a'))));
}
// Loop for the BFS Traversal
while (!q.isEmpty()) {
// Stores the current
// lexicographically smallest
// String of min characters
String cur = q.peek();
q.remove();
// If the current String is
// not present as a subString
// of the given String
if (!collection.contains(cur)) {
// Print Answer
System.out.print(cur +"\n");
return;
}
// Append characters from [a-z]
// to the back of String cur
// and push into the queue.
for (int i = 0; i < 26; ++i) {
cur+=String.valueOf((char)((i + 'a')));
q.add(cur);
cur=cur.substring(0,cur.length()-1);
}
}
}
// Driver Code
public static void main(String[] args)
{
String S = "aabacdefghijklmnopqrstuvwxyz";
int N = S.length();
lexicographicalSmallestString(S.toCharArray(), N);
}
}
// This code is contributed by shikhasingrajput
# python implementation of the above approach
from queue import Queue
# Function to find the lexicographically
# smallest string of minimum characters
# not present as substring in string S
def lexicographicalSmallestString(S, n):
# Set which stores all substrings
# of the string S
collection = set()
# Constructing all substrings of S
for i in range(0, n):
cur = ""
for j in range(i, n):
cur += (S[j])
# Inserting the current
# substring to set
collection.add(cur)
q = Queue()
# Initializing BFS queue
for i in range(0, 26):
q.put(chr(i + ord('a')))
# Loop for the BFS Traversal
while (not q.empty()):
# Stores the current
# lexicographically smallest
# string of min characters
cur = q.get()
# If the current string is
# not present as a substring
# of the given string
if (not (cur in collection)):
# Print Answer
print(cur)
return
# Append characters from [a-z]
# to the back of string cur
# and push into the queue.
for i in range(0, 26):
q.put((cur + chr(i+ord('a'))))
# Driver Code
if __name__ == "__main__":
S = "aabacdefghijklmnopqrstuvwxyz"
N = len(S)
lexicographicalSmallestString(S, N)
# This code is contributed by rakeshsahni
// C# implementation of the above approach
using System;
using System.Collections.Generic;
public class GFG{
// Function to find the lexicographically
// smallest String of minimum characters
// not present as subString in String S
static void lexicographicalSmallestString(char[] S, int n)
{
// Set which stores all subStrings
// of the String S
HashSet<String> collection = new HashSet<String>();
// Constructing all subStrings of S
for (int i = 0; i < n; ++i) {
String cur = "";
for (int j = i; j < n; ++j) {
cur += (S[j]);
// Inserting the current
// subString to set
collection.Add(cur);
}
}
Queue<String> q = new Queue<String>();
// Initializing BFS queue
for (int i = 0; i < 26; ++i) {
q.Enqueue(String.Join("",(char)((i + 'a'))));
}
// Loop for the BFS Traversal
while (q.Count != 0) {
// Stores the current
// lexicographically smallest
// String of min characters
String cur = q.Peek();
q.Dequeue();
// If the current String is
// not present as a subString
// of the given String
if (!collection.Contains(cur)) {
// Print Answer
Console.Write(cur +"\n");
return;
}
// Append characters from [a-z]
// to the back of String cur
// and push into the queue.
for (int i = 0; i < 26; ++i) {
cur += String.Join("",(char)((i + 'a')));
q.Enqueue(cur);
cur=cur.Substring(0,cur.Length-1);
}
}
}
// Driver Code
public static void Main(String[] args)
{
String S = "aabacdefghijklmnopqrstuvwxyz";
int N = S.Length;
lexicographicalSmallestString(S.ToCharArray(), N);
}
}
// This code is contributed by 29AjayKumar
// Javascript implementation of the above approach
// Function to find the lexicographically
// smallest string of minimum characters
// not present as substring in string S
function lexicographicalSmallestString(S, n)
{
// Set which stores all substrings
// of the string S
let collection = new Set();
// Constructing all substrings of S
for (let i = 0; i < n; ++i) {
let cur = ""
for (let j = i; j < n; ++j) {
cur += S[j];
// Inserting the current
// substring to set
collection.add(cur);
}
}
let q = [];
// Initializing BFS queue
for (let i = 0; i < 26; ++i) {
q.push(String.fromCharCode('a'.charCodeAt(0) + i));
}
// Loop for the BFS Traversal
while (q.length) {
// Stores the current
// lexicographically smallest
// string of min characters
let cur = q[0];
q.shift();
// If the current string is
// not present as a substring
// of the given string
if (!collection.has(cur)) {
// Print Answer
document.write(cur + '<br>');
return;
}
// Append characters from [a-z]
// to the back of string cur
// and push into the queue.
for (let i = 0; i < 26; ++i) {
q.push(cur + (String.fromCharCode(i + 'a'.charCodeAt(0))));
}
}
}
// Driver Code
let S = "aabacdefghijklmnopqrstuvwxyz";
let N = S.length;
lexicographicalSmallestString(S, N);
// This code is contributed by gfgking.
Time Complexity: O(N2 * log N)
Auxiliary Space: O(N2)
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