Sort a string lexicographically by reversing a substring

Given a string S consisting of N lowercase characters, the task is to find the starting and the ending indices ( 0-based indexing ) of the substring of the given string S that needed to be reversed to make the string S sorted. If it is not possible to sort the given string S by reversing any substring, then print “-1”.

Examples:

Input: S = “abcyxuz”
Output: 3 5
Explanation: Reversing the substring from indices [3, 5] modifies the string to “abcuxyz”, which is sorted.
Therefore, print 3 and 5.

Input: S = “GFG”
Output: 0 1

Naive Approach: The simplest approach to solve the given problem is to generate all possible substring of the given string S and if there exists any substring such reversing it makes the string sorted, then print the indices of that substrings. Otherwise, print “-1”.

Time Complexity: O(N³)
Auxiliary Space: O(1)

Efficient Approach: The above approach can also be optimized based on the observation that to sort the string by only reversing one substring, the original string must be in one of the following formats:

• Decreasing string
• Increasing substring + Decreasing substring
• Decreasing substring + Increasing substring
• Increasing substring + Decreasing substring + Increasing substring

Follow the steps below to solve the problem:

• Initialize two variables, say start and end as -1, that stores the starting and ending indices of the substring to be reversed respectively.
• Initialize a variable, say flag as 1, that stores if it is possible to sort the string or not.
• Iterate over the range [1, N] and perform the following operations:
  • If the characters S[i] is less than characters S[i – 1] then find the index of the right boundary of the decreasing substring starting from the index (i – 1) and store it in end.
  • Check if reversing the substring S[i – 1, end] makes the string sorted or not. If found to be false then print “-1” and return. Otherwise, mark the flag as false.
  • After completing the above steps update the value of i with the right boundary of the substring.
  • If the characters S[i] is less than characters S[i – 1] and the flag is false, then print “-1” and return.
• If the start is equal to -1, then update the value of start and end as 1.
• After completing the above steps, print the value of start and end as the result.

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 substring
// in S required to be reversed
bool adjust(string& S, int& i,
            int& start, int& end)
{
    // Stores the size of the string
    int N = S.length();

    // Stores the starting point
    // of the substring
    start = i - 1;

    // Iterate over the string S
    // while i < N
    while (i < N && S[i] < S[i - 1]) {

        // Increment the value of i
        i++;
    }

    // Stores the ending index of
    // the substring
    end = i - 1;

    // If start <= 0 or i >= N
    if (start <= 0 && i >= N)
        return true;

    // If start >= 1 and i <= N
    if (start >= 1 && i <= N) {

        // Return the boolean value
        return (S[end] >= S[start - 1]
                && S[start] <= S[i]);
    }

    // If start >= 1
    if (start >= 1) {

        // Return the boolean value
        return S[end] >= S[start - 1];
    }

    // If i < N
    if (i < N) {

        // Return true if S[start]
        // is less than or equal to
        // S[i]
        return S[start] <= S[i];
    }

    // Otherwise
    return false;
}

// Function to check if it is possible
// to sort the string or not
void isPossible(string& S, int N)
{
    // Stores the starting and the
    // ending index of substring
    int start = -1, end = -1;

    // Stores whether it is possible
    // to sort the substring
    bool flag = true;

    // Traverse the range [1, N]
    for (int i = 1; i < N; i++) {

        // If S[i] is less than S[i-1]
        if (S[i] < S[i - 1]) {

            // If flag stores true
            if (flag) {

                // If adjust(S, i, start,
                // end) return false
                if (adjust(S, i, start, end)
                    == false) {

                    // Print -1
                    cout << -1 << endl;
                    return;
                }

                // Unset the flag
                flag = false;
            }

            // Otherwise
            else {

                // Print -1
                cout << -1 << endl;
                return;
            }
        }
    }

    // If start is equal to -1
    if (start == -1) {
        // Update start and end
        start = end = 1;
    }

    // Print the value of start
    // and end
    cout << start << " "
         << end << "\n";
}

// Driver Code
int main()
{
    string S = "abcyxuz";
    int N = S.length();
    isPossible(S, N);

    return 0;
}

Java

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

class GFG{

static int i, start, end;

// Function to find the substring
// in S required to be reversed
static boolean adjust(String S)
{

    // Stores the size of the string
    int N = S.length();

    // Stores the starting point
    // of the substring
    start = i - 1;

    // Iterate over the string S
    // while i < N
    while (i < N && S.charAt(i) <
                    S.charAt(i - 1))
    {

        // Increment the value of i
        i++;
    }

    // Stores the ending index of
    // the substring
    end = i - 1;

    // If start <= 0 or i >= N
    if (start <= 0 && i >= N)
        return true;

    // If start >= 1 and i <= N
    if (start >= 1 && i <= N)
    {

        // Return the boolean value
        return (S.charAt(end) >= S.charAt(start - 1) &&
                S.charAt(start) <= S.charAt(i));
    }

    // If start >= 1
    if (start >= 1)
    {

        // Return the boolean value
        return S.charAt(end) >= S.charAt(start - 1);
    }

    // If i < N
    if (i < N)
    {

        // Return true if S[start]
        // is less than or equal to
        // S[i]
        return S.charAt(start) <= S.charAt(i);
    }

    // Otherwise
    return false;
}

// Function to check if it is possible
// to sort the string or not
static void isPossible(String S, int N)
{

    // Stores the starting and the
    // ending index of substring
    start = -1; end = -1;

    // Stores whether it is possible
    // to sort the substring
    boolean flag = true;

    // Traverse the range [1, N]
    for(i = 1; i < N; i++)
    {

        // If S[i] is less than S[i-1]
        if (S.charAt(i) < S.charAt(i - 1))
        {

            // If flag stores true
            if (flag)
            {

                // If adjust(S, i, start,
                // end) return false
                if (adjust(S) == false)
                {

                    // Print -1
                    System.out.println(-1);
                    return;
                }

                // Unset the flag
                flag = false;
            }

            // Otherwise
            else
            {

                // Print -1
                System.out.println(-1);
                return;
            }
        }
    }

    // If start is equal to -1
    if (start == -1)
    {

        // Update start and end
        start = end = 1;
    }

    // Print the value of start
   System.out.println(start + " " + end);
}

// Driver code
public static void main(String[] args)
{
    String S = "abcyxuz";
    int N = S.length();
    isPossible(S, N);
}
}

// This code is contributed by offbeat

Python3

# Python3 program for the above approach

# Function to find the substring
# in S required to be reversed
def adjust(S, i, start, end):

    # Stores the size of the string
    N = len(S)

    # Stores the starting point
    # of the substring
    start = i - 1

    # Iterate over the string S
    # while i < N
    while (i < N and S[i] < S[i - 1]):

        # Increment the value of i
        i += 1

    # Stores the ending index of
    # the substring
    end = i - 1

    # If start <= 0 or i >= N
    if (start <= 0 and i >= N):
        return True,start,i,end

    # If start >= 1 and i <= N
    if (start >= 1 and i <= N):

        # Return the boolean value
        return (S[end] >= S[start - 1] and S[start] <= S[i]),start,i,end

    # If start >= 1
    if (start >= 1):

        # Return the boolean value
        return (S[end] >= S[start - 1]),start,i,end

    # If i < N
    if (i < N):

        # Return true if S[start]
        # is less than or equal to
        # S[i]
        return (S[start] <= S[i]),start,i,end

    # Otherwise
    return False,start,i,end

# Function to check if it is possible
# to sort the string or not
def isPossible(S, N):

    # global start,end,i
    # Stores the starting and the
    # ending index of substring
    start, end = -1, -1

    # Stores whether it is possible
    # to sort the substring
    flag = True

    # Traverse the range [1, N]
    i = 1
    while i < N:

        # If S[i] is less than S[i-1]
        if (S[i] < S[i - 1]):

            # If flag stores true
            if (flag):

                # If adjust(S, i, start,
                # end) return false
                f, start, i, end = adjust(S, i, start, end)
                if (f== False):
                    # Pr-1
                    print(-1)
                    return

                # Unset the flag
                flag = False
            # Otherwise
            else:

                # Pr-1
                print(-1)
                return
        i += 1

    # If start is equal to -1
    if (start == -1):
        # Update start and end
        start, end = 1, 1

    # Print the value of start
    # and end
    print(start, end)

# Driver Code
if __name__ == '__main__':
    S = "abcyxuz"
    N = len(S)
    isPossible(S, N)

    # This code is contributed by mohit kumar 29.

C#

// C# program for the above approach
using System;

class GFG{

static int i, start, end;

// Function to find the substring
// in S required to be reversed
static bool adjust(string S)
{

    // Stores the size of the string
    int N = S.Length;

    // Stores the starting point
    // of the substring
    start = i - 1;

    // Iterate over the string S
    // while i < N
    while (i < N && S[i] <  S[i - 1])
    {

        // Increment the value of i
        i++;
    }

    // Stores the ending index of
    // the substring
    end = i - 1;

    // If start <= 0 or i >= N
    if (start <= 0 && i >= N)
        return true;

    // If start >= 1 and i <= N
    if (start >= 1 && i <= N)
    {

        // Return the boolean value
        return (S[end] >= S[start - 1] &&
                S[start] <= S[i]);
    }

    // If start >= 1
    if (start >= 1)
    {

        // Return the boolean value
        return S[end] >= S[start - 1];
    }

    // If i < N
    if (i < N)
    {

        // Return true if S[start]
        // is less than or equal to
        // S[i]
        return S[start] <= S[i];
    }

    // Otherwise
    return false;
}

// Function to check if it is possible
// to sort the string or not
static void isPossible(string S, int N)
{

    // Stores the starting and the
    // ending index of substring
    start = -1; end = -1;

    // Stores whether it is possible
    // to sort the substring
    bool flag = true;

    // Traverse the range [1, N]
    for(i = 1; i < N; i++)
    {

        // If S[i] is less than S[i-1]
        if (S[i] < S[i - 1])
        {

            // If flag stores true
            if (flag)
            {

                // If adjust(S, i, start,
                // end) return false
                if (adjust(S) == false)
                {

                    // Print -1
                    Console.WriteLine(-1);
                    return;
                }

                // Unset the flag
                flag = false;
            }

            // Otherwise
            else
            {

                // Print -1
                 Console.WriteLine(-1);
                return;
            }
        }
    }

    // If start is equal to -1
    if (start == -1)
    {

        // Update start and end
        start = end = 1;
    }

    // Print the value of start
    Console.WriteLine(start + " " + end);
}

// Driver code
static void Main()
{
    string S = "abcyxuz";
    int N = S.Length;

    isPossible(S, N);
}
}

// This code is contributed by SoumikMondal

Javascript

<script>

      // JavaScript program for the above approach
      var i, start, end;

      // Function to find the substring
      // in S required to be reversed
      function adjust(S) {
        // Stores the size of the string
        var N = S.length;

        // Stores the starting point
        // of the substring
        start = i - 1;

        // Iterate over the string S
        // while i < N
        while (i < N && S[i] < S[i - 1]) {
          // Increment the value of i
          i++;
        }

        // Stores the ending index of
        // the substring
        end = i - 1;

        // If start <= 0 or i >= N
        if (start <= 0 && i >= N) return true;

        // If start >= 1 and i <= N
        if (start >= 1 && i <= N) {
          // Return the boolean value
          return S[end] >= S[start - 1] && S[start] <= S[i];
        }

        // If start >= 1
        if (start >= 1) {
          // Return the boolean value
          return S[end] >= S[start - 1];
        }

        // If i < N
        if (i < N) {
          // Return true if S[start]
          // is less than or equal to
          // S[i]
          return S[start] <= S[i];
        }

        // Otherwise
        return false;
      }

      // Function to check if it is possible
      // to sort the string or not
      function isPossible(S, N) {
        // Stores the starting and the
        // ending index of substring
        start = -1;
        end = -1;

        // Stores whether it is possible
        // to sort the substring
        var flag = true;

        // Traverse the range [1, N]
        for (i = 1; i < N; i++) {
          // If S[i] is less than S[i-1]
          if (S[i] < S[i - 1]) {
            // If flag stores true
            if (flag) {
              // If adjust(S, i, start,
              // end) return false
              if (adjust(S) === false) {
                // Print -1
                document.write(-1);
                return;
              }

              // Unset the flag
              flag = false;
            }

            // Otherwise
            else {
              // Print -1
              document.write(-1);
              return;
            }
          }
        }

        // If start is equal to -1
        if (start === -1) {
          // Update start and end
          start = end = 1;
        }

        // Print the value of start
        document.write(start + " " + end + "<br>");
      }

      // Driver code
      var S = "abcyxuz";
      var N = S.length;

      isPossible(S, N);

</script>

Output:

3 5

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