Given two sentences S1 and S2, the task is to check if the sentences can be made equal by inserting at most one sentence(possibly, empty) into any one of the two sentences.
Examples:
Input : S1 = “Start practicing on neveropen”, S2 =”Start GeeksforGeeeks”
Output :
True
Explanation: “practicing on” can be inserted between “Start” and “neveropen” in s2 to make it equal to S1.Input: S1= “New Delhi is capital of INDIA”, S2 = “is capital of”
Output:
False
Approach: The following observations help in solving the problem:
- If the sizes of two sentences are equal, but they themselves are not the same, they cannot be made equal.
- After the longest common prefix and the longest common suffix of the two sentences are removed, if at least one of them is empty, it means that they can be made equal.
The problem can be solved with the help of deques. Follow the steps below to solve the problem:
- Check if the size of S1 and S2 are equal. If they are equal, do the following:
- If S1 is equal to S2, return true.
- Otherwise, return false.
- Initialize two deques X and Y.
- Push all words of S1 into X.
- Push all words of S2 into Y.
- While the fronts of X and Y are the same, pop from the fronts of both X and Y.
- While the backs of X and Y are the same, pop from the backs of both X and Y.
- Check if any one of X or Y is empty. If any of them is empty, return true.
- Otherwise, return false.
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <bits/stdc++.h> using namespace std; // Function to check whether // two sentences can be made equal // by inserting at most // one sentence in one of them bool areSimilar(string S1, string S2) { // size of sentence S1 int N = S1.size(); // size of sentence S2 int M = S2.size(); // check if S1 and S2 // are of equal sizes if (N == M) { // if both sentences are // the same, return true if (S1 == S2) return true ; // Otherwise, return false return false ; } // Declare 2 deques X and Y deque<string> X, Y; // insert ' ' at the end of both // sentences so that the last // word can be identified S1.push_back( ' ' ); S2.push_back( ' ' ); string temp = "" ; // traverse the sentence S1 for ( int i = 0; i < N + 1; i++) { // push temp in deque // when a space comes in sentence // i.e a word has been formed if (S1[i] == ' ' ) { X.push_back(temp); temp = "" ; } else { // temp stores words // of the sentence temp += S1[i]; } } // traverse the sentence S1 for ( int i = 0; i < M + 1; i++) { // push temp in deque // when a space comes in sentence // i.e a word has been formed if (S2[i] == ' ' ) { Y.push_back(temp); temp = "" ; } else { // temp stores words of the sentence temp += S2[i]; } } // check for prefixes of both sentences while (X.size() > 0 && Y.size() > 0 && X.front() == Y.front()) { // pop the prefix from both // deques till they are equal X.pop_front(); Y.pop_front(); } // check for suffixes of both sentences while (X.size() > 0 && Y.size() > 0 && X.back() == Y.back()) { // pop the suffix from both deques // till they are equal X.pop_back(); Y.pop_back(); } // if any of the deques is empty // return true if (X.size() == 0 || Y.size() == 0) return true ; // if both the deques are // not empty return false return false ; } // Driver code int main() { // Input string S1 = "Start practicing on neveropen" ; string S2 = "Start neveropen" ; // function call if (areSimilar(S1, S2)) cout << "True" << endl; else cout << "False" << endl; return 0; } |
Java
import java.util.*; public class Main { // Function to check whether // two sentences can be made equal // by inserting at most // one sentence in one of them public static boolean areSimilar(String S1, String S2) { // size of sentence S1 int N = S1.length(); // size of sentence S2 int M = S2.length(); // check if S1 and S2 // are of equal sizes if (N == M) { // if both sentences are // the same, return true if (S1.equals(S2)) return true ; // Otherwise, return false return false ; } // Declare 2 deques X and Y Deque<String> X = new LinkedList<>(); Deque<String> Y = new LinkedList<>(); // insert ' ' at the end of both // sentences so that the last // word can be identified S1 += " " ; S2 += " " ; String temp = "" ; // traverse the sentence S1 for ( int i = 0 ; i < N + 1 ; i++) { // push temp in deque // when a space comes in sentence // i.e a word has been formed if (S1.charAt(i) == ' ' ) { X.addLast(temp); temp = "" ; } else { // temp stores words // of the sentence temp += S1.charAt(i); } } // traverse the sentence S2 for ( int i = 0 ; i < M + 1 ; i++) { // push temp in deque // when a space comes in sentence // i.e a word has been formed if (S2.charAt(i) == ' ' ) { Y.addLast(temp); temp = "" ; } else { // temp stores words of the sentence temp += S2.charAt(i); } } // check for prefixes of both sentences while (!X.isEmpty() && !Y.isEmpty() && X.peekFirst().equals(Y.peekFirst())) { // pop the prefix from both // deques till they are equal X.removeFirst(); Y.removeFirst(); } // check for suffixes of both sentences while (!X.isEmpty() && !Y.isEmpty() && X.peekLast().equals(Y.peekLast())) { // pop the suffix from both deques // till they are equal X.removeLast(); Y.removeLast(); } // if any of the deques is empty // return true if (X.isEmpty() || Y.isEmpty()) return true ; // if both the deques are // not empty return false return false ; } // Driver code public static void main(String[] args) { // Input String S1 = "Start practicing on neveropen" ; String S2 = "Start neveropen" ; // function call if (areSimilar(S1, S2)) System.out.println( "True" ); else System.out.println( "False" ); } } |
Python3
# Python3 program for the above approach from collections import deque # Function to check whether # two sentences can be made equal # by inserting at most # one sentence in one of them def areSimilar(S1, S2): S1 = [i for i in S1] S2 = [i for i in S2] # Size of sentence S1 N = len (S1) # Size of sentence S2 M = len (S2) # Check if S1 and S2 # are of equal sizes if (N = = M): # If both sentences are # the same, return True if (S1 = = S2): return True # Otherwise, return false return False # Declare 2 deques X and Y X, Y = deque(), deque() # Insert ' ' at the end of both # sentences so that the last # word can be identified S1.append( ' ' ) S2.append( ' ' ) temp = "" # Traverse the sentence S1 for i in range (N + 1 ): # Push temp in deque # when a space comes in sentence # i.e a word has been formed if (S1[i] = = ' ' ): X.append(temp) temp = "" else : # temp stores words # of the sentence temp + = S1[i] # Traverse the sentence S1 for i in range (M + 1 ): # Push temp in deque # when a space comes in sentence # i.e a word has been formed if (S2[i] = = ' ' ): Y.append(temp) temp = "" else : # temp stores words of the sentence temp + = S2[i] # Check for prefixes of both sentences while ( len (X) > 0 and len (Y) > 0 and X[ 0 ] = = Y[ 0 ]): # Pop the prefix from both # deques till they are equal X.popleft() Y.popleft() # Check for suffixes of both sentences while ( len (X) > 0 and len (Y) > 0 and X[ - 1 ] = = Y[ - 1 ]): # Pop the suffix from both deques # till they are equal X.pop() Y.pop() # If any of the deques is empty # return True if ( len (X) = = 0 or len (Y) = = 0 ): return True # If both the deques are # not empty return false return False # Driver code if __name__ = = '__main__' : # Input S1 = "Start practicing on neveropen" S2 = "Start neveropen" # Function call if (areSimilar(S1, S2)): print ( "True" ) else : print ( "False" ) # This code is contributed by mohit kumar 29 |
C#
using System; using System.Collections.Generic; class Program { // Function to check whether // two sentences can be made equal // by inserting at most // one sentence in one of them static bool AreSimilar( string S1, string S2) { // size of sentence S1 int N = S1.Length; // size of sentence S2 int M = S2.Length; // check if S1 and S2 // are of equal sizes if (N == M) { // if both sentences are // the same, return true if (S1 == S2) return true ; // Otherwise, return false return false ; } // Declare 2 deques X and Y Queue< string > X = new Queue< string >(); Queue< string > Y = new Queue< string >(); // insert ' ' at the end of both // sentences so that the last // word can be identified S1 += ' ' ; S2 += ' ' ; string temp = "" ; // traverse the sentence S1 for ( int i = 0; i < N + 1; i++) { // push temp in deque // when a space comes in sentence // i.e a word has been formed if (S1[i] == ' ' ) { X.Enqueue(temp); temp = "" ; } else { // temp stores words // of the sentence temp += S1[i]; } } // traverse the sentence S2 for ( int i = 0; i < M + 1; i++) { // push temp in deque // when a space comes in sentence // i.e a word has been formed if (S2[i] == ' ' ) { Y.Enqueue(temp); temp = "" ; } else { // temp stores words of the sentence temp += S2[i]; } } // check for prefixes of both sentences while (X.Count > 0 && Y.Count > 0 && X.Peek() == Y.Peek()) { // pop the prefix from both // deques till they are equal X.Dequeue(); Y.Dequeue(); } // check for suffixes of both sentences while (X.Count > 0 && Y.Count > 0 && X.ToArray()[X.Count - 1] == Y.ToArray()[Y.Count - 1]) { // pop the suffix from both deques // till they are equal X.Dequeue(); Y.Dequeue(); } // if any of the deques is empty // return true if (X.Count == 0 || Y.Count == 0) return true ; // if both the deques are // not empty return false return false ; } // Driver code static void Main( string [] args) { // Input string S1 = "Start practicing on neveropen" ; string S2 = "Start neveropen" ; // function call if (AreSimilar(S1, S2)) Console.WriteLine( "True" ); else Console.WriteLine( "False" ); Console.ReadLine(); } } |
Javascript
// JavaScript program for the above approach // Function to check whether // two sentences can be made equal // by inserting at most // one sentence in one of them function areSimilar(S1, S2) { S1 = S1.split( '' ); S2 = S2.split( '' ); // Size of sentence S1 const N = S1.length; // Size of sentence S2 const M = S2.length; // Check if S1 and S2 // are of equal sizes if (N === M) { // If both sentences are // the same, return true if (S1.join( '' ) === S2.join( '' )) { return true ; } // Otherwise, return false return false ; } // Declare 2 deques X and Y const X = [], Y = []; // Insert ' ' at the end of both // sentences so that the last // word can be identified S1.push( ' ' ); S2.push( ' ' ); let temp = "" ; // Traverse the sentence S1 for (let i = 0; i < N + 1; i++) { // Push temp in deque // when a space comes in sentence // i.e a word has been formed if (S1[i] === ' ' ) { X.push(temp); temp = "" ; } else { // temp stores words // of the sentence temp += S1[i]; } } // Traverse the sentence S1 for (let i = 0; i < M + 1; i++) { // Push temp in deque // when a space comes in sentence // i.e a word has been formed if (S2[i] === ' ' ) { Y.push(temp); temp = "" ; } else { // temp stores words of the sentence temp += S2[i]; } } // Check for prefixes of both sentences while (X.length > 0 && Y.length > 0 && X[0] === Y[0]) { // Pop the prefix from both // deques till they are equal X.shift(); Y.shift(); } // Check for suffixes of both sentences while (X.length > 0 && Y.length > 0 && X[X.length - 1] === Y[Y.length - 1]) { // Pop the suffix from both deques // till they are equal X.pop(); Y.pop(); } // If any of the deques is empty // return true if (X.length === 0 || Y.length === 0) { return true ; } // If both the deques are // not empty return false return false ; } // Driver code const S1 = "Start practicing on neveropen" ; const S2 = "Start neveropen" ; // Function call if (areSimilar(S1, S2)) { console.log( "True" ); } else { console.log( "False" ); } // Contributed by adityashae15 |
True
Time Complexity: O(N+M), where N and M are the sizes of S1 and S2 respectively.
Auxiliary Space: O(N+M)
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