Maximum length prefix such that frequency of each character is atmost number of characters with minimum frequency

Given a string S, the task is to find the prefix of string S with the maximum possible length such that frequency of each character in the prefix is at most the number of characters in S with minimum frequency.

Examples: 

Input: S = ‘aabcdaab’ 
Output: aabcd 
Explanation: 
Frequency of characters in the given string – 
{a: 4, b: 2, c: 1, d: 1} 
Minimum frequency in 1 and the count of minimum frequency is 2, 
So frequency of each character in the prefix can be at most 2.

Input: S = ‘aaabc’ 
Output: aa 
Explanation: 
Frequency of characters in the given string – 
{a: 3, b: 1, c: 1} 
Minimum frequency in 1 and the count of minimum frequency is 2, 
So frequency of each character in the prefix can be at most 2. 

Approach: 



  • Initialize a hash-map to store the frequency of the characters.
  • Iterate over the string and increment the frequency of the character in the hash-map.
  • Find the minimum occurred character in the string and the count of such characters whose frequency is minimum.
  • Initialize another hash-map to store the frequency of the characters of the possible prefix string.
  • Finally, Iterate over the string from start and increment the count of the characters until the frequency of any characters is not greater than the count of the minimum frequency.

Below is the implementation of the above approach:

Python3

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# Python3 implementation to find the
# prefix of the string such that
# occurrence of each character is
# atmost the count of minimum
# frequency in the string
 
# Function to find the maximum
# possible prefix of the string
def MaxPrefix(string):
     
    # Hash map to store the frequency
    # of the characters in the string
    Dict = {}
    maxprefix = 0
     
    # Iterate over the string to find
    # the occurence of each Character
    for i in string:
        Dict[i] = Dict.get(i, 0) + 1
     
    # Minimum frequency of the Characters
    minfrequency = min(Dict.values())
    countminFrequency = 0
     
    # Loop to find the count of minimum
    # frequency in the hash-map
    for x in Dict:
        if (Dict[x] == minfrequency):
            countminFrequency += 1
     
    mapper = {}
    indi = 0
     
    # Loop to find the maximum possible
    # length of the prefix in the string   
    for i in string:
        mapper[i] = mapper.get(i, 0) + 1
         
        # Condition to check if the frequency
        # is greater than minimum possible freq
        if (mapper[i] > countminFrequency):
            break
        indi += 1
             
    # maxprefix string and its length.
    print(string[:indi])
 
# Driver code
if __name__ == '__main__':
     
    # String is initialize.
    str = 'aabcdaab'
    # str is passed in MaxPrefix function.
    MaxPrefix(str)

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C#

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// C# implementation to find the
// prefix of the s such that
// occurrence of each character is
// atmost the count of minimum
// frequency in the s
using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
 
class GFG{
  
// Function to find the maximum
// possible prefix of the s
static void MaxPrefix(string s)
{   
     
    // Hash map to store the frequency
    // of the characters in the s
    Dictionary<char,
               int> Dict = new Dictionary<char,
                                          int>();
 
    // Iterate over the s to find
    // the occurence of each Character
    foreach(char i in s)
    {
        if (Dict.ContainsKey(i))
        {
            Dict[i]++;
        }
        else
        {
            Dict[i] = 1;
        }
    }
     
    int minfrequency = Int32.MaxValue;
      
    // Minimum frequency of the Characters
    foreach(int x in Dict.Values.ToList())
    {
        minfrequency = Math.Min(minfrequency, x);   
    }
     
    int countminFrequency = 0;
      
    // Loop to find the count of minimum
    // frequency in the hash-map
    foreach(char x in Dict.Keys.ToList())
    {
        if (Dict[x] == minfrequency)
            countminFrequency += 1;
    }
     
    Dictionary<char,
               int> mapper = new Dictionary<char,
                                            int>();
    int indi = 0;
      
    // Loop to find the maximum possible
    // length of the prefix in the s
    foreach(char i in s)
    {
        if (mapper.ContainsKey(i))
        {
            mapper[i]++;
        }
        else
        {
            mapper[i] = 1;
        }
          
        // Condition to check if the frequency
        // is greater than minimum possible freq
        if (mapper[i] > countminFrequency)
            break;
             
        indi += 1;
    }
              
    // maxprefix s and its length.
    Console.Write(s.Substring(0, indi));
}
 
// Driver Code
public static void Main(string[] args)
{
     
    // s is initialize.
    string str = "aabcdaab";
     
    // str is passed in
    // MaxPrefix function.
    MaxPrefix(str);
}
}
 
// This code is contributed by rutvik_56

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Output: 

aabcd









 

Performance Analysis: 

  • Time Complexity: In the above-given approach, there is one loop to find the frequency of each character in the string which takes O(N) time in the worst case. Therefore, the time complexity for this approach will be O(N).
  • Space Complexity: In the above-given approach, there is extra space used to store the frequency of characters. Therefore, the space complexity for the above approach will be O(N)

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