Given a binary string S of length N, the task is to find the smallest string possible by removing all occurrences of substrings “01” and “11”. After removal of any substring, concatenate the remaining parts of the string.
Examples:
Input: S = “1010”
Output: 2
Explanation: Removal of substring “01” modifies string S to “10”.Input: S = “111”
Output: 1
Stack-based Approach: Refer to the previous article to find the length of the smallest string possible by given operations.
Time Complexity: O(N)
Auxiliary Space: O(N)
Space-Optimized Approach: The above approach can be space-optimized by only storing the length of the characters not removed. Follow the steps below to solve the problem:
- Initialize a variable, say st as 0, to store the length of the smallest string possible.
- Iterate over the characters of the string S and perform the following steps:
- If st is greater than 0 and S[i] is equal to ‘1‘, then pop the last element by decrementing st by 1.
- Otherwise, increment st by 1.
- Finally, after completing the above steps, print the answer obtained in st.
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <bits/stdc++.h> using namespace std; // Function to find the length of // the smallest string possible by // removing substrings "01" and "11" int shortestString(string S, int N) { // Stores the length of // the smallest string int st = 0; // Traverse the string S for ( int i = 0; i < N; i++) { // If st is greater // than 0 and S[i] is '1' if (st && S[i] == '1' ) { // Delete the last // character and // decrement st by 1 st--; } // Otherwise else { // Increment st by 1 st++; } } // Return the answer in st return st; } // Driver Code int main() { // Input string S = "1010" ; int N = S.length(); // Function call cout << shortestString(S, N); return 0; } |
Java
// Java program for the above approach public class GFG_JAVA { // Function to find the length of // the smallest string possible by // removing substrings "01" and "11" static int shortestString(String S, int N) { // Stores the length of // the smallest string int st = 0 ; // Traverse the string S for ( int i = 0 ; i < N; i++) { // If st is greater // than 0 and S[i] is '1' if (st > 0 && S.charAt(i) == '1' ) { // Delete the last // character and // decrement st by 1 st--; } // Otherwise else { // Increment st by 1 st++; } } // Return the answer in st return st; } // Driver code public static void main(String[] args) { // Input String S = "1010" ; int N = S.length(); // Function call System.out.println(shortestString(S, N)); } } // This code is contributed by abhinavjain194 |
Python3
# Python3 program for the above approach # Function to find the length of # the smallest string possible by # removing substrings "01" and "11" def shortestString(S, N) : # Stores the length of # the smallest string st = 0 ; # Traverse the string S for i in range (N) : # If st is greater # than 0 and S[i] is '1' if (st and S[i] = = '1' ) : # Delete the last # character and # decrement st by 1 st - = 1 ; # Otherwise else : # Increment st by 1 st + = 1 ; # Return the answer in st return st; # Driver Code if __name__ = = "__main__" : # Input S = "1010" ; N = len (S); # Function call print (shortestString(S, N)); # This code is contributed by AnkThon |
C#
// C# program for the above approach using System; public class GFG_JAVA { // Function to find the length of // the smallest string possible by // removing substrings "01" and "11" static int shortestString( string S, int N) { // Stores the length of // the smallest string int st = 0; // Traverse the string S for ( int i = 0; i < N; i++) { // If st is greater // than 0 and S[i] is '1' if (st > 0 && S[i] == '1' ) { // Delete the last // character and // decrement st by 1 st--; } // Otherwise else { // Increment st by 1 st++; } } // Return the answer in st return st; } // Driver code public static void Main( string [] args) { // Input string S = "1010" ; int N = S.Length; // Function call Console.WriteLine(shortestString(S, N)); } } // This code is contributed by AnkThon |
Javascript
<script> // Javascript program for the above approach // Function to find the length of // the smallest string possible by // removing substrings "01" and "11" function shortestString(S, N) { // Stores the length of // the smallest string let st = 0; // Traverse the string S for (let i = 0; i < N; i++) { // If st is greater // than 0 and S[i] is '1' if (st > 0 && S[i] == '1' ) { // Delete the last // character and // decrement st by 1 st--; } // Otherwise else { // Increment st by 1 st++; } } // Return the answer in st return st; } // Input let S = "1010" ; let N = S.length; // Function call document.write(shortestString(S, N)); // This code is contributed by divyeshrabadiya07. </script> |
2
Time Complexity: O(N)
Auxiliary Space: O(1)
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