Lexicographically largest string possible by reversing substrings having even number of 1s

Given a binary string S, the task is to convert the given string S to its lexicographic maximum form by reversing substrings having an even number of 1s.

Examples:

Input: S = “10101”
Output: 11010
Explanation:
Reversing the substring {S[0], …, S[2]} modifies S to “10101”. 
Reversing the substring {S[1], …, S[4]} modifies S to “11010”. 
Now, any other substring cannot be chosen as each will either have odd number of 1s or will be lexicographically smaller than the previous string. Thus, 11010 is the lexicographically largest string that can be performed.

Input: S = “0101”
Output: 1010

Approach: The idea is to start from the first index and traverse the string till the total number of 1s in the string becomes even. As soon as an index is found where there is exactly an even number of 1s, reverse the string from the starting index to the end index. Repeat this process for every index to get the lexicographically largest string.

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 lexicographically
// maximum string by reversing substrings
// having even numbers of 1s
void lexicographicallyMax(string s)
{
    // Store size of string
    int n = s.size();

    // Traverse the string
    for (int i = 0; i < n; i++) {

        // Count the number of 1s
        int count = 0;

        // Stores the starting index
        int beg = i;

        // Stores the end index
        int end = i;

        // Increment count, when 1
        // is encountered
        if (s[i] == '1')
            count++;

        // Traverse the remaining string
        for (int j = i + 1; j < n; j++) {
            if (s[j] == '1')
                count++;

            if (count % 2 == 0
                && count != 0) {
                end = j;
                break;
            }
        }

        // Reverse the string from
        // starting and end index
        reverse(s.begin() + beg,
                s.begin() + end + 1);
    }

    // Printing the string
    cout << s << "\n";
}

// Driver Code
int main()
{
    string S = "0101";
    lexicographicallyMax(S);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to find the lexicographically
// maximum string by reversing substrings
// having even numbers of 1s
static void lexicographicallyMax(String s)
{

    // Store size of string
    int n = s.length();

    // Traverse the string
    for(int i = 0; i < n; i++)
    {

        // Count the number of 1s
        int count = 0;

        // Stores the starting index
        int beg = i;

        // Stores the end index
        int end = i;

        // Increment count, when 1
        // is encountered
        if (s.charAt(i) == '1')
            count++;

        // Traverse the remaining string
        for(int j = i + 1; j < n; j++)
        {
            if (s.charAt(j) == '1')
                count++;

            if (count % 2 == 0 &&
                count != 0)
            {
                end = j;
                break;
            }
        }

        // Reverse the string from
        // starting and end index
        s = reverse(s, beg, end + 1);
    }

    // Printing the string
   System.out.println(s);
}

static String reverse(String s, int beg, int end)
{
    StringBuilder x = new StringBuilder("");

    for(int i = 0; i < beg; i++)
        x.append(s.charAt(i));
    for(int i = end - 1; i >= beg; i--)
        x.append(s.charAt(i));
    for(int i = end; i < s.length(); i++)
        x.append(s.charAt(i));

    return x.toString();
}

// Driver Code
public static void main(String args[])
{
    String S = "0101";

    lexicographicallyMax(S);
}
}

// This code is contributed by jyoti369

Python3

# Python3 program for the above approach

# Function to find the lexicographically
# maximum string by reversing substrings
# having even numbers of 1s
def lexicographicallyMax(s):

    # Store size of string
    n = len(s)

    # Traverse the string
    for i in range(n):

        # Count the number of 1s
        count = 0

        # Stores the starting index
        beg = i

        # Stores the end index
        end = i

        # Increment count, when 1
        # is encountered
        if (s[i] == '1'):
            count += 1

        # Traverse the remaining string
        for j in range(i + 1, n):
            if (s[j] == '1'):
                count += 1

            if (count % 2 == 0 and count != 0):
                end = j
                break

        # temp is for Reverse the string from
        # starting and end index
        temp = s[beg : end + 1]
        temp = temp[::-1]
        s = s[0 : beg] + temp + s[end + 1 :]

    # Printing the string
    print(s)

# Driver Code
S = "0101"

lexicographicallyMax(S)

# This code is contributed by avanitrachhadiya2155

C#

// C# program for the above approach
using System;
using System.Text;
class GFG
{

// Function to find the lexicographically
// maximum string by reversing substrings
// having even numbers of 1s
static void lexicographicallyMax(String s)
{

    // Store size of string
    int n = s.Length;

    // Traverse the string
    for(int i = 0; i < n; i++)
    {

        // Count the number of 1s
        int count = 0;

        // Stores the starting index
        int beg = i;

        // Stores the end index
        int end = i;

        // Increment count, when 1
        // is encountered
        if (s[i] == '1')
            count++;

        // Traverse the remaining string
        for(int j = i + 1; j < n; j++)
        {
            if (s[j] == '1')
                count++;
            if (count % 2 == 0 &&
                count != 0)
            {
                end = j;
                break;
            }
        }

        // Reverse the string from
        // starting and end index
        s = reverse(s, beg, end + 1);
    }

    // Printing the string
   Console.WriteLine(s);
}

static String reverse(String s, int beg, int end)
{
    StringBuilder x = new StringBuilder("");

    for(int i = 0; i < beg; i++)
        x.Append(s[i]);
    for(int i = end - 1; i >= beg; i--)
        x.Append(s[i]);
    for(int i = end; i < s.Length; i++)
        x.Append(s[i]);

    return x.ToString();
}

// Driver Code
public static void Main(String []args)
{
    String S = "0101";
    lexicographicallyMax(S);
}
}


// This code is contributed by Princi Singh

Javascript

<script>

// JavaScript program for the above approach

// Function to find the lexicographically
// maximum string by reversing substrings
// having even numbers of 1s
function lexicographicallyMax(s)
{
    // Store size of string
    var n = s.length;

    // Traverse the string
    for (var i = 0; i < n; i++) {

        // Count the number of 1s
        var count = 0;

        // Stores the starting index
        var beg = i;

        // Stores the end index
        var end = i;

        // Increment count, when 1
        // is encountered
        if (s[i] == '1')
            count++;

        // Traverse the remaining string
        for (var j = i + 1; j < n; j++) {
            if (s[j] == '1')
                count++;

            if (count % 2 == 0
                && count != 0) {
                end = j;
                break;
            }
        }

        // Reverse the string from
        // starting and end index
        for(var i = beg; i<parseInt((end+1)/2);i++)
        {
            let temp = s[i] ;
            s[i] = s[end - i+1] ;
            s[end -i+1 ] = temp;
        }
    }

    // Printing the string
    document.write( s.join("") + "<br>");
}

// Driver Code
var S = "0101".split('');
lexicographicallyMax(S);

</script>

Output:

1010

Time Complexity: O(N²)
Auxiliary Space: O(1)