Largest string obtained in Dictionary order after deleting K characters

Given string str of length N and an integer K, the task is to return the largest string in Dictionary Order by erasing K characters from that string.

A largest string Dictionary order is the last string when strings are arranged in alphabetical order.

Examples:

Input: str = “ritz” K = 2
Output: tz
Explanation:
There are 6 possible ways of deleting two characters from s: “ri”, “rt”, “rz”, “it”, “iz”, “tz”. 
Among these strings “tz” is the largest in dictionary order. 
Thus “tz” is the desired output.

Input: str = “jackie” K = 2
Output: jkie
Explanation:
The characters “a” and “c” are deleted to get the largest possible string.

Naive Approach: The idea is to find all the subsequence of the given string length N – K. Store those subsequences in a list. There will be ⁿC_m Such sequences. After the above steps print the largest string in alphabetical order stored in the list.

Time Complexity:  O(2^N-K)

Efficient Approach: The idea is to use a Deque. Below are the steps:

1. Store all the characters of the string in the deque.
2. Traverse the given string and for each character in the string keep popping the characters from deque if it is less than the last character stored in the deque. Perform this operation until K is non-zero.
3. Now after the above operations, insert the current character in the deque.
4. After the above operations, the string formed by the characters stored in the deque is the resultant 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 largest
// string after deleting k characters
string largestString(int n, int k, string s)
{

    // Deque dq used to find the
    // largest string in dictionary
    // after deleting k characters
    deque<char> deq;

    // Iterate till the length
    // of the string
    for(int i = 0; i < n; ++i)
    {

        // Condition for popping
        // characters from deque
        while (deq.size() > 0 &&
               deq.back() < s[i] &&
                        k > 0)
        {
            deq.pop_front();
            k--;
        }

        deq.push_back(s[i]);
    }

    // To store the resultant string
    string st = "";

    // To form resultant string
    for(char c : deq)
        st = st + c;

    // Return the resultant string
    return st;
}

// Driver code
int main()
{
    int n = 4;
    int k = 2;

    // Given String
    string sc = "ritz";

    // Function call
    string result = largestString(n, k, sc);

    // Print the answer
    cout << result << endl;

    return 0;
}

// This code is contributed by divyeshrabadiya07

Java

// Java program for the above approach

import java.util.ArrayDeque;
import java.util.Deque;
import java.util.Scanner;
import java.io.IOException;

public class GFG {

    // Function to find the largest
    // string after deleting k characters
    public static String
    largestString(int n, int k, String sc)
    {
        char[] s = sc.toCharArray();

        // Deque dq used to find the
        // largest string in dictionary
        // after deleting k characters
        Deque<Character> deq
            = new ArrayDeque<>();

        // Iterate till the length
        // of the string
        for (int i = 0; i < n; ++i) {

            // Condition for popping
            // characters from deque
            while (deq.size() > 0
                   && deq.getLast() < s[i]
                   && k > 0) {
                deq.pollLast();
                k--;
            }

            deq.add(s[i]);
        }

        // To store the resultant string
        String st = "";

        // To form resultant string
        for (char c : deq)
            st = st + Character.toString(c);

        // Return the resultant string
        return st;
    }

    // Driver Code
    public static void main(String[] args)
        throws IOException
    {
        int n = 4;
        int k = 2;

        // Given String
        String sc = "ritz";

        // Function call
        String result = largestString(n, k, sc);

        // Print the answer
        System.out.println(result);
    }
}

Python3

# Python3 program for the above approach
from collections import deque

# Function to find the largest
# string after deleting k characters
def largestString(n, k, sc):

    s = [i for i in sc]

    # Deque dq used to find the
    # largest string in dictionary
    # after deleting k characters
    deq = deque()

    # Iterate till the length
    # of the string
    for i in range(n):

        # Condition for popping
        # characters from deque
        while (len(deq) > 0 and
                deq[-1] < s[i] and
                      k > 0):
            deq.popleft()
            k -= 1

        deq.append(s[i])

    # To store the resultant string
    st = ""

    # To form resultant string
    for c in deq:
        st = st + c

    # Return the resultant string
    return st

# Driver Code
if __name__ == '__main__':

    n = 4
    k = 2

    # Given String
    sc = "ritz"

    # Function call
    result = largestString(n, k, sc)

    # Print the answer
    print(result)

# This code is contributed by mohit kumar 29

C#

using System;
using System.Linq;
using System.Collections.Generic;

class GFG
{
  // Function to find the largest
  // string after deleting k characters
  public static string LargestString(int n, int k, string sc)
  {
    char[] s = sc.ToCharArray();

    // Deque dq used to find the
    // largest string in dictionary
    // after deleting k characters
    List<char> deq = new List<char>();

    // Iterate till the length
    // of the string
    for (int i = 0; i < n; ++i)
    {
      // Condition for popping
      // characters from deque
      while (deq.Count > 0
             && deq[deq.Count - 1] < s[i]
             && k > 0)
      {
        deq.RemoveAt(deq.Count - 1);
        k--;
      }

      deq.Add(s[i]);
    }

    // To store the resultant string
    string st = "";

    // To form resultant string
    foreach (char c in deq)
      st = st + c.ToString();

    // Return the resultant string
    return st;
  }

  // Driver Code
  public static void Main(string[] args)
  {
    int n = 4;
    int k = 2;

    // Given String
    string sc = "ritz";

    // Function call
    string result = LargestString(n, k, sc);

    // Print the answer
    Console.WriteLine(result);
  }
}

Javascript

<script>

// Javascript program for the above approach

// Function to find the largest
// string after deleting k characters
function largestString(n, k, s)
{

    // Deque dq used to find the
    // largest string in dictionary
    // after deleting k characters
    var deq = [];

    // Iterate till the length
    // of the string
    for(var i = 0; i < n; ++i)
    {

        // Condition for popping
        // characters from deque
        while (deq.length > 0 &&
               deq[deq.length - 1] < s[i] &&
                            k > 0)
        {
            deq.shift();
            k--;
        }
        deq.push(s[i]);
    }

    // To store the resultant string
    var st = "";

    // To form resultant string
    deq.forEach(c => {
        st = st + c;
    });

    // Return the resultant string
    return st;
}

// Driver code
var n = 4;
var k = 2;

// Given String
var sc = "ritz";

// Function call
var result = largestString(n, k, sc);

// Print the answer
document.write(result);

// This code is contributed by rutvik_56

</script>

Output:

tz

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