Length of longest subsequence whose difference between maximum and minimum ASCII value of characters is exactly one

Given a string S consisting of lowercase English alphabets, the task is to find the length of the longest subsequence from the given string such that the difference between the largest and smallest ASCII value is exactly 1.

Examples:

Input: S = “acbbebcg”
Output: 5
Explanation: The longest subsequence of required type is “cbbbc”, whose length is 5.
The difference between largest (‘c’) and smallest (‘b’) ASCII values is c – b = 99 – 98 = 1, which is minimum possible.

Input: S = “abcd”
Output: 2
Explanation: The longest subsequence of the required type is “ab”, whose length is 2. Other possible subsequences are “bc” and “cd”.
The difference between largest(‘b’) and smallest(‘a’) ASCII values is b – a = 98 – 97 = 1.

Naive Approach: The simplest approach to solve the problem is to generate all possible subsequences of the given string S and print the length of the subsequence which is of maximum length and having a difference between ASCII values of the largest and smallest character is exactly equal to 1. 

Time Complexity: O(N * 2^N)
Auxiliary Space: O(N)

Efficient Approach: To optimize the above approach, the main idea is to use a Map to optimize the above approach. Follow the steps below to solve the problem:

• Initialize a variable, say maxLength, that stores the maximum length of the resultant subsequence.
• Store the frequency of characters in a Map, say M.
• Traverse the string and for each character, say ch, check if there exists character c with ASCII value (ch – 1) in the map M or not. If found to be true, then update maxLength as the maximum of maxLength and (M[ch] + M[ch – 1]).
• After completing the above steps, print the value of maxLength 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 maximum length of
// subsequence having difference of ASCII
// value of longest and smallest character as 1
int maximumLengthSubsequence(string str)
{
    // Stores frequency of characters
    unordered_map<char, int> mp;

    // Iterate over characters
    // of the string
    for (char ch : str) {
        mp[ch]++;
    }
    // Stores the resultant
    // length of subsequence
    int ans = 0;

    for (char ch : str) {
        // Check if there exists any
        // elements with ASCII value
        // one less than character ch
        if (mp.count(ch - 1)) {
            // Size of current subsequence

            int curr_max = mp[ch] + mp[ch - 1];
            // Update the value of ans
            ans = max(ans, curr_max);
        }
    }

    // Print the resultant count
    cout << ans;
}

// Driver Code
int main()
{
    string S = "acbbebcg";
    maximumLengthSubsequence(S);

    return 0;
}

Java

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

class GFG{

// Function to find the maximum length of
// subsequence having difference of ASCII
// value of longest and smallest character as 1
static void maximumLengthSubsequence(String str)
{

    // Stores frequency of characters
    HashMap<Character, Integer> mp = new HashMap<>();
    for(char ch : str.toCharArray())
    {
        mp.put(ch, mp.getOrDefault(ch, 0) + 1);
    }

    // Stores the resultant
    // length of subsequence
    int ans = 0;

    for(char ch : str.toCharArray())
    {

        // Check if there exists any
        // elements with ASCII value
        // one less than character ch
        if (mp.containsKey((char)(ch - 1)))
        {

            // Size of current subsequence
            int curr_max = mp.get(ch) +
                    mp.get((char)(ch - 1));

            // Update the value of ans
            ans = Math.max(ans, curr_max);
        }
    }

    // Print the resultant count
    System.out.println(ans);
}

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

    maximumLengthSubsequence(S);
}
}

// This code is contributed by aadityapburujwale

Python3

# Python3 program for the above approach

# Function to find the maximum length of
# subsequence having difference of ASCII
# value of longest and smallest character as 1
def maximumLengthSubsequence(str):

    # Stores frequency of characters
    mp = {}

    # Iterate over characters
    # of the string
    for ch in str:
        if ch in mp.keys():
            mp[ch] += 1
        else:
            mp[ch] = 1

    # Stores the resultant
    # length of subsequence
    ans = 0

    for ch in str:

        # Check if there exists any
        # elements with ASCII value
        # one less than character ch
        if chr(ord(ch) - 1) in mp.keys():

            # Size of current subsequence
            curr_max = mp[ch]

            if chr(ord(ch) - 1) in mp.keys():
                 curr_max += mp[chr(ord(ch) - 1)]

            # Update the value of ans
            ans = max(ans, curr_max)

    # Print the resultant count
    print(ans)

# Driver Code
S = "acbbebcg"

maximumLengthSubsequence(S)

# This code is contributed by Stream_Cipher

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

public class GFG
{

// Function to find the maximum length of
// subsequence having difference of ASCII
// value of longest and smallest character as 1
static void maximumLengthSubsequence(String str)
{

    // Stores frequency of characters
    Dictionary<char, int> mp = new Dictionary<char, int>();
    foreach(char ch in str.ToCharArray())
    {
        if(mp.ContainsKey(ch))
            mp[ch] = mp[ch] + 1;
        else
            mp.Add(ch, 1);
    }

    // Stores the resultant
    // length of subsequence
    int ans = 0;
    foreach(char ch in str.ToCharArray())
    {

        // Check if there exists any
        // elements with ASCII value
        // one less than character ch
        if (mp.ContainsKey((char)(ch - 1)))
        {

            // Size of current subsequence
            int curr_max = mp[ch] +
                    mp[(char)(ch - 1)];

            // Update the value of ans
            ans = Math.Max(ans, curr_max);
        }
    }

    // Print the resultant count
    Console.WriteLine(ans);
}

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

// This code is contributed by Amit Katiyar

Javascript

<script>
      // JavaScript program for the above approach
      // Function to find the maximum length of
      // subsequence having difference of ASCII
      // value of longest and smallest character as 1
      function maximumLengthSubsequence(str) {
        // Stores frequency of characters
        var mp = {};

        var temp = str.split("");
        for (const ch of temp) {
          if (mp.hasOwnProperty(ch)) mp[ch] = mp[ch] + 1;
          else mp[ch] = 1;
        }

        // Stores the resultant
        // length of subsequence
        var ans = 0;
        for (const ch of temp) {
          // Check if there exists any
          // elements with ASCII value
          // one less than character ch
          if (mp.hasOwnProperty(String.fromCharCode(ch.charCodeAt(0) - 1))) {
            // Size of current subsequence
            var curr_max =
              mp[ch] + mp[String.fromCharCode(ch.charCodeAt(0) - 1)];

            // Update the value of ans
            ans = Math.max(ans, curr_max);
          }
        }

        // Print the resultant count
        document.write(ans);
      }

      // Driver Code
      var S = "acbbebcg";
      maximumLengthSubsequence(S);

      // This code is contributed by rdtank.
    </script>

Output

5

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