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Check if a Binary String can be sorted in decreasing order by removing non-adjacent characters
• Difficulty Level : Hard
• Last Updated : 10 May, 2021

Given a binary string S of size N, the task is to check if the binary string S can be sorted in decreasing order by removing any number of the non-adjacent characters. If it is possible to sort the string in decreasing order, then print “Yes”. Otherwise, print “No”.

Examples:

Input: S = “10101011011”
Output: Yes
Explanation:
After removing the non-adjacent characters at indices 1, 3, 5, and 8 modifies the string to “1111111”, which is sorted in decreasing order. Therefore, print “Yes”.

Input: S = “0011”
Output: No

Approach: The given problem can be solved based on the observations that if there exist two adjacent characters having 1s and then there exists adjacent characters having 0s then it is impossible to sort the string by removing the non-adjacent characters. Follow the steps below to solve the problem:

• Initialize a boolean variable, say flag as true that stores the status whether the given string can be sorted or not.
• Traverse the given string S from the end and if there exists any pairs of adjacent characters having values 1s then stored the second index of 1 in a variable say idx and break out of the loop.
• Traverse the given string S again from the back over the range [idx, 0] and if there exists any pairs of adjacent characters having values 0s then update the value of flag as false and break out of the loop.
• After completing the above steps, if the value of flag is true, then print “Yes”. Otherwise, print “No”.

Below is the implementation of the above approach:

## C++

 `// C++ programm for the above appraoch` `#include ``using` `namespace` `std;` `// Function to sort the given string in``// decreasing order by removing the non``// adajcent characters``string canSortString(string S, ``int` `N)``{``    ``// Keeps the track whether the``    ``// string can be sorted or not``    ``int` `flag = 1;` `    ``int` `i, j;` `    ``// Traverse the given string S``    ``for` `(i = N - 2; i >= 0; i--) {` `        ``// Check if S[i] and``        ``// S[i + 1] are both '1'``        ``if` `(S[i] == ``'1'``            ``&& S[i + 1] == ``'1'``) {``            ``break``;``        ``}``    ``}` `    ``// Traverse the string S from``    ``// the indices i to 0``    ``for` `(``int` `j = i; j >= 0; j--) {` `        ``// If S[j] and S[j + 1] is``        ``// equal to 0``        ``if` `(S[j] == ``'0'``            ``&& S[j + 1] == ``'0'``) {` `            ``// Mark flag false``            ``flag = 0;``            ``break``;``        ``}``    ``}` `    ``// If flag is 0, then it is not``    ``// possible to sort the string``    ``if` `(flag == 0) {``        ``return` `"No"``;``    ``}` `    ``// Otherwise``    ``else` `{``        ``return` `"Yes"``;``    ``}``}` `// Driver Code``int` `main()``{``    ``string S = ``"10101011011"``;``    ``int` `N = S.length();``    ``cout << canSortString(S, N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;` `class` `GFG``{` `  ``// Function to sort the given string in``// decreasing order by removing the non``// adajcent characters``static` `String canSortString(String S, ``int` `N)``{``  ` `    ``// Keeps the track whether the``    ``// string can be sorted or not``    ``int` `flag = ``1``;` `    ``int` `i, j;` `    ``// Traverse the given string S``    ``for` `(i = N - ``2``; i >= ``0``; i--) {` `        ``// Check if S[i] and``        ``// S[i + 1] are both '1'``        ``if` `(S.charAt(i) == ``'1'``            ``&& S.charAt(i + ``1``) == ``'1'``) {``            ``break``;``        ``}``    ``}` `    ``// Traverse the string S from``    ``// the indices i to 0``    ``for` `( j = i; j >= ``0``; j--) {` `        ``// If S[j] and S[j + 1] is``        ``// equal to 0``        ``if` `(S.charAt(j) == ``'0'``            ``&& S.charAt(j + ``1``) == ``'0'``) {` `            ``// Mark flag false``            ``flag = ``0``;``            ``break``;``        ``}``    ``}` `    ``// If flag is 0, then it is not``    ``// possible to sort the string``    ``if` `(flag == ``0``) {``        ``return` `"No"``;``    ``}` `    ``// Otherwise``    ``else` `{``        ``return` `"Yes"``;``    ``}``}` `    ``public` `static` `void` `main (String[] args) {``      ``String S = ``"10101011011"``;``    ``int` `N = S.length();``    ``System.out.println(canSortString(S, N));``  ` `    ``}``}` `// This code is contributed by offbeat`

## Python3

 `# Python3 program for the above appraoch` `# Function to sort the given string in``# decreasing order by removing the non``# adajcent characters``def` `canSortString(S, N):``    ` `    ``# Keeps the track whether the``    ``# string can be sorted or not``    ``flag ``=` `1` `    ``# Traverse the given string S``    ``i ``=` `N ``-` `2``    ` `    ``while``(i >``=` `0``):``        ` `        ``# Check if S[i] and``        ``# S[i + 1] are both '1'``        ``if` `(S[i] ``=``=` `'1'` `and` `S[i ``+` `1``] ``=``=` `'1'``):``            ``break``        ` `        ``i ``-``=` `1` `    ``# Traverse the string S from``    ``# the indices i to 0``    ``j ``=` `i``    ` `    ``while``(j >``=` `0``):``        ` `        ``# If S[j] and S[j + 1] is``        ``# equal to 0``        ``if` `(S[j] ``=``=` `'0'` `and` `S[j ``+` `1``] ``=``=` `'0'``):``            ` `            ``# Mark flag false``            ``flag ``=` `0``            ``break``        ` `        ``j ``-``=` `1` `    ``# If flag is 0, then it is not``    ``# possible to sort the string``    ``if` `(flag ``=``=` `0``):``        ``return` `"No"` `    ``# Otherwise``    ``else``:``        ``return` `"Yes"` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``S ``=` `"10101011011"``    ``N ``=` `len``(S)``    ` `    ``print``(canSortString(S, N))` `# This code is contributed by ipg2016107`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to sort the given string in``// decreasing order by removing the non``// adajcent characters``static` `string` `canSortString(``string` `S, ``int` `N)``{``    ` `    ``// Keeps the track whether the``    ``// string can be sorted or not``    ``int` `flag = 1;` `    ``int` `i, j;` `    ``// Traverse the given string S``    ``for``(i = N - 2; i >= 0; i--)``    ``{``        ` `        ``// Check if S[i] and``        ``// S[i + 1] are both '1'``        ``if` `(S[i] == ``'1'` `&& S[i + 1] == ``'1'``)``        ``{``            ``break``;``        ``}``    ``}` `    ``// Traverse the string S from``    ``// the indices i to 0``    ``for``(j = i; j >= 0; j--)``    ``{``        ` `        ``// If S[j] and S[j + 1] is``        ``// equal to 0``        ``if` `(S[j] == ``'0'` `&& S[j + 1] == ``'0'``)``        ``{``            ` `            ``// Mark flag false``            ``flag = 0;``            ``break``;``        ``}``    ``}` `    ``// If flag is 0, then it is not``    ``// possible to sort the string``    ``if` `(flag == 0)``    ``{``        ``return` `"No"``;``    ``}` `    ``// Otherwise``    ``else``    ``{``        ``return` `"Yes"``;``    ``}``}` `// Driver code``public` `static` `void` `Main(``string``[] args)``{``    ``string` `S = ``"10101011011"``;``    ``int` `N = S.Length;``    ` `    ``Console.WriteLine(canSortString(S, N));``}``}` `// This code is contributed by ukasp`

## Javascript

 ``
Output:
`Yes`

Time Complexity: O(N)
Auxiliary Space: O(1)

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