Given string str of length N, the task is to remove all the characters from the string whose frequencies are prime.
Examples:
Input: str = “geeksforgeeks”
Output: eeforee
Explanation:
The frequencies of characters is: { g=2, e=4, k=2, s=2, f=1, o=1, r=1}
So, g, k and s are the characters with prime frequencies so, they are removed from the string.
The resultant string is “eeforee”Input: str = “abcdef”
Output: abcdef
Explanation:
Since all the characters are unique with frequency as 1, so no character is removed.
Naive Approach: The simplest approach to solve this problem is to find the frequencies of every distinct character present in the string and for each character, check if its frequency is Prime or not. If the frequency is found to be prime, skip that character. Otherwise, append it to the new string formed.
Time Complexity: O( N 3/2)
Auxiliary Space: O(N)
Efficient Approach: The above approach can be optimized by using the Sieve of Eratosthenes to precompute Prime Numbers. Follow the steps below to solve the problem:
- Using Sieve of Eratosthenes, generate all prime numbers up to N and store them in the array prime[].
- Initialize a Map and store the frequency of each character.
- Then, traverse the string and find out which characters have prime frequencies with the help of the map and prime[] array.
- Ignore all those characters which have prime frequencies and store the rest in a new string.
- After the above steps, print the new string.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to perform the sieve of // eratosthenes algorithm void SieveOfEratosthenes( bool * prime, int n)
{ // Initialize all entries in
// prime[] as true
for ( int i = 0; i <= n; i++) {
prime[i] = true ;
}
// Initialize 0 and 1 as non prime
prime[0] = prime[1] = false ;
// Traversing the prime array
for ( int i = 2; i * i <= n; i++) {
// If i is prime
if (prime[i] == true ) {
// All multiples of i must
// be marked false as they
// are non prime
for ( int j = 2; i * j <= n; j++) {
prime[i * j] = false ;
}
}
}
} // Function to remove characters which // have prime frequency in the string void removePrimeFrequencies(string s)
{ // Length of the string
int n = s.length();
// Create a boolean array prime
bool prime[n + 1];
// Sieve of Eratosthenes
SieveOfEratosthenes(prime, n);
// Stores the frequency of character
unordered_map< char , int > m;
// Storing the frequencies
for ( int i = 0; i < s.length(); i++) {
m[s[i]]++;
}
// New string that will be formed
string new_string = "" ;
// Removing the characters which
// have prime frequencies
for ( int i = 0; i < s.length(); i++) {
// If the character has
// prime frequency then skip
if (prime[m[s[i]]])
continue ;
// Else concatenate the
// character to the new string
new_string += s[i];
}
// Print the modified string
cout << new_string;
} // Driver Code int main()
{ string str = "geeksforgeeks" ;
// Function Call
removePrimeFrequencies(str);
return 0;
} |
// Java program for the above approach import java.util.*;
class GFG{
// Function to perform the sieve of // eratosthenes algorithm static void SieveOfEratosthenes( boolean [] prime,
int n)
{ // Initialize all entries in
// prime[] as true
for ( int i = 0 ; i <= n; i++)
{
prime[i] = true ;
}
// Initialize 0 and 1 as non prime
prime[ 0 ] = prime[ 1 ] = false ;
// Traversing the prime array
for ( int i = 2 ; i * i <= n; i++)
{
// If i is prime
if (prime[i] == true )
{
// All multiples of i must
// be marked false as they
// are non prime
for ( int j = 2 ; i * j <= n; j++)
{
prime[i * j] = false ;
}
}
}
} // Function to remove characters which // have prime frequency in the String static void removePrimeFrequencies( char [] s)
{ // Length of the String
int n = s.length;
// Create a boolean array prime
boolean []prime = new boolean [n + 1 ];
// Sieve of Eratosthenes
SieveOfEratosthenes(prime, n);
// Stores the frequency of character
HashMap<Character, Integer> m = new HashMap<>();
// Storing the frequencies
for ( int i = 0 ; i < s.length; i++)
{
if (m.containsKey(s[i]))
{
m.put(s[i], m.get(s[i]) + 1 );
}
else
{
m.put(s[i], 1 );
}
}
// New String that will be formed
String new_String = "" ;
// Removing the characters which
// have prime frequencies
for ( int i = 0 ; i < s.length; i++)
{
// If the character has
// prime frequency then skip
if (prime[m.get(s[i])])
continue ;
// Else concatenate the
// character to the new String
new_String += s[i];
}
// Print the modified String
System.out.print(new_String);
} // Driver Code public static void main(String[] args)
{ String str = "geeksforgeeks" ;
// Function Call
removePrimeFrequencies(str.toCharArray());
} } // This code is contributed by aashish1995 |
# Python3 program for the above approach # Function to perform the sieve of # eratosthenes algorithm def SieveOfEratosthenes(prime, n) :
# Initialize all entries in
# prime[] as true
for i in range (n + 1 ) :
prime[i] = True
# Initialize 0 and 1 as non prime
prime[ 0 ] = prime[ 1 ] = False
# Traversing the prime array
i = 2
while i * i < = n :
# If i is prime
if (prime[i] = = True ) :
# All multiples of i must
# be marked false as they
# are non prime
j = 2
while i * j < = n :
prime[i * j] = False
j + = 1
i + = 1
# Function to remove characters which # have prime frequency in the String def removePrimeFrequencies(s) :
# Length of the String
n = len (s)
# Create a bool array prime
prime = [ False ] * (n + 1 )
# Sieve of Eratosthenes
SieveOfEratosthenes(prime, n)
# Stores the frequency of character
m = {}
# Storing the frequencies
for i in range ( len (s)) :
if s[i] in m :
m[s[i]] + = 1 else :
m[s[i]] = 1
# New String that will be formed
new_String = ""
# Removing the characters which
# have prime frequencies
for i in range ( len (s)) :
# If the character has
# prime frequency then skip
if (prime[m[s[i]]]) :
continue
# Else concatenate the
# character to the new String
new_String + = s[i]
# Print the modified String
print (new_String, end = "")
Str = "geeksforgeeks"
# Function Call removePrimeFrequencies( list ( Str ))
# This code is contributed by divyesh072019 |
// C# program for the above approach using System;
using System.Collections.Generic;
class GFG{
// Function to perform the sieve of // eratosthenes algorithm static void SieveOfEratosthenes( bool [] prime,
int n)
{ // Initialize all entries in
// prime[] as true
for ( int i = 0; i <= n; i++)
{
prime[i] = true ;
}
// Initialize 0 and 1 as non prime
prime[0] = prime[1] = false ;
// Traversing the prime array
for ( int i = 2; i * i <= n; i++)
{
// If i is prime
if (prime[i] == true )
{
// All multiples of i must
// be marked false as they
// are non prime
for ( int j = 2; i * j <= n; j++)
{
prime[i * j] = false ;
}
}
}
} // Function to remove characters which // have prime frequency in the String static void removePrimeFrequencies( char [] s)
{ // Length of the String
int n = s.Length;
// Create a bool array prime
bool []prime = new bool [n + 1];
// Sieve of Eratosthenes
SieveOfEratosthenes(prime, n);
// Stores the frequency of character
Dictionary< char ,
int > m = new Dictionary< char ,
int >();
// Storing the frequencies
for ( int i = 0; i < s.Length; i++)
{
if (m.ContainsKey(s[i]))
{
m[s[i]]++;
}
else
{
m.Add(s[i], 1);
}
}
// New String that will be formed
String new_String = "" ;
// Removing the characters which
// have prime frequencies
for ( int i = 0; i < s.Length; i++)
{
// If the character has
// prime frequency then skip
if (prime[m[s[i]]])
continue ;
// Else concatenate the
// character to the new String
new_String += s[i];
}
// Print the modified String
Console.Write(new_String);
} // Driver Code public static void Main(String[] args)
{ String str = "geeksforgeeks" ;
// Function Call
removePrimeFrequencies(str.ToCharArray());
} } // This code is contributed by aashish1995 |
<script> // JavaScript program for the above approach // Function to perform the sieve of // eratosthenes algorithm function SieveOfEratosthenes(prime, n)
{ // Initialize all entries in
// prime[] as true
for (let i = 0; i <= n; i++) {
prime[i] = true ;
}
// Initialize 0 and 1 as non prime
prime[0] = prime[1] = false ;
// Traversing the prime array
for (let i = 2; i * i <= n; i++) {
// If i is prime
if (prime[i] == true ) {
// All multiples of i must
// be marked false as they
// are non prime
for (let j = 2; i * j <= n; j++) {
prime[i * j] = false ;
}
}
}
} // Function to remove characters which // have prime frequency in the string function removePrimeFrequencies( s)
{ // Length of the string
var n = s.length;
// Create a boolean array prime
var prime = new Array(n + 1);
// Sieve of Eratosthenes
SieveOfEratosthenes(prime, n);
// Stores the frequency of character
var m = {};
for (let i =0;i<s.length;i++)
m[s[i]] = 0;
// Storing the frequencies
for (let i = 0; i < s.length; i++) {
m[s[i]]++;
}
// New string that will be formed
var new_string = "" ;
// Removing the characters which
// have prime frequencies
for (let i = 0; i < s.length; i++) {
// If the character has
// prime frequency then skip
if (prime[m[s[i]]])
continue ;
// Else concatenate the
// character to the new string
new_string += s[i];
}
// Print the modified string
console.log( new_string);
} // Driver Code str = "geeksforgeeks" ;
// Function Call removePrimeFrequencies(str); // This code is contributed by ukasp. </script> |
eeforee
Time Complexity: O(N*log (log N))
Auxiliary Space: O(N)