Construct a string that has exactly K subsequences from given string

Last Updated : 18 May, 2021

Given a string str and an integer K, the task is to find a string S such that it has exactly K subsequences of given string str.
Examples:

Input: str = "gfg", K = 10
Output: gggggffg
Explanation:
There are 10 possible subsequence of the given string "gggggffg". They are:
1. gggggffg
2. gggggffg
3. gggggffg
4. gggggffg
5. gggggffg
6. gggggffg
7. gggggffg
8. gggggffg
9. gggggffg
10. gggggffg.
Input: str = "code", K = 20
Output: cccccoodde
Explanation:
There are 20 possible subsequence of the string "cccccoodde".

Approach:
To solve the problem mentioned above we have to follow the steps given below:

The idea is to find the prime factors of K and store the prime factors(say factors).
Create an empty array count of the size of the given string to store the count of each character in the resultant string s. Initialize the array with 1.
Now pop elements from the list factors and multiply to each position of array in a cyclic way until the list becomes empty. Finally, we have the count of each character of str in the array.
Iterate in the array count[] and append the number of characters for each character ch to the resultant string s.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
#include <iostream>
using namespace std;

// Function that computes the string s
void printSubsequenceString(string str,
                            long long k)
{
    // Length of the given string str
    int n = str.size();
    int i;

    // List that stores all the prime
    // factors of given k
    vector<long long> factors;

    // Find the prime factors
    for (long long i = 2;
         i <= sqrt(k); i++) {

        while (k % i == 0) {
            factors.push_back(i);
            k /= i;
        }
    }
    if (k > 1)
        factors.push_back(k);

    // Initialize the count of each
    // character position as 1
    vector<long long> count(n, 1);

    int index = 0;

    // Loop until the list
    // becomes empty
    while (factors.size() > 0) {

        // Increase the character
        // count by multiplying it
        // with the prime factor
        count[index++] *= factors.back();
        factors.pop_back();

        // If we reach end then again
        // start from beginning
        if (index == n)
            index = 0;
    }

    // Store the output
    string s;

    for (i = 0; i < n; i++) {
        while (count[i]-- > 0) {
            s += str[i];
        }
    }

    // Print the string
    cout << s;
}

// Driver code
int main()
{
    // Given String
    string str = "code";

    long long k = 20;

    // Function Call
    printSubsequenceString(str, k);
    return 0;
}

Java

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

// Function that computes the String s 
static void printSubsequenceString(String str, 
                                      int k) 
{ 
    // Length of the given String str 
    int n = str.length(); 
    int i; 

    // List that stores all the prime 
    // factors of given k 
    Vector<Integer> factors = new Vector<Integer>(); 

    // Find the prime factors 
    for (i = 2; i <= Math.sqrt(k); i++) 
    { 
        while (k % i == 0) 
        { 
            factors.add(i); 
            k /= i; 
        } 
    } 
    if (k > 1) 
        factors.add(k); 

    // Initialize the count of each 
    // character position as 1 
    int []count = new int[n]; 
    Arrays.fill(count, 1);
    int index = 0; 

    // Loop until the list 
    // becomes empty 
    while (factors.size() > 0) 
    { 

        // Increase the character 
        // count by multiplying it 
        // with the prime factor 
        count[index++] *= factors.get(factors.size() - 1); 
        factors.remove(factors.get(factors.size() - 1)); 

        // If we reach end then again 
        // start from beginning 
        if (index == n) 
            index = 0; 
    } 

    // Store the output 
    String s = ""; 

    for (i = 0; i < n; i++) 
    { 
        while (count[i]-- > 0) 
        { 
            s += str.charAt(i); 
        } 
    } 

    // Print the String 
    System.out.print(s); 
} 

// Driver code 
public static void main(String[] args) 
{ 
    // Given String 
    String str = "code"; 

    int k = 20; 

    // Function Call 
    printSubsequenceString(str, k); 
}
} 

// This code is contributed by sapnasingh4991

Python3

# Python3 program for 
# the above approach
import math

# Function that computes 
# the string s
def printSubsequenceString(st, k):
    # Length of the given 
    # string str
    n = len(st)

    # List that stores 
    # all the prime
    # factors of given k
    factors = []
  
    # Find the prime factors
    sqt = (int(math.sqrt(k)))
    for i in range (2, sqt + 1):

        while (k % i == 0):
            factors.append(i)
            k //= i
   
    if (k > 1):
        factors.append(k)

    # Initialize the count of each
    # character position as 1
    count = [1] * n

    index = 0

    # Loop until the list
    # becomes empty
    while (len(factors) > 0):

        # Increase the character
        # count by multiplying it
        # with the prime factor
        count[index] *= factors[-1]
        factors.pop()
        index += 1

        # If we reach end then again
        # start from beginning
        if (index == n):
            index = 0
            
    # store output
    s = ""
    for i in range (n):
        while (count[i] > 0):
            s += st[i]
            count[i] -= 1  
       
    # Print the string
    print (s)

# Driver code
if __name__ == "__main__":
  
    # Given String
    st = "code"

    k = 20

    # Function Call
    printSubsequenceString(st, k)
    
# This code is contributed by Chitranayal

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

class GFG{ 

// Function that computes the String s 
static void printSubsequenceString(String str, 
                                      int k) 
{ 
    // Length of the given String str 
    int n = str.Length; 
    int i; 

    // List that stores all the prime 
    // factors of given k 
    List<int> factors = new List<int>(); 

    // Find the prime factors 
    for (i = 2; i <= Math.Sqrt(k); i++) 
    { 
        while (k % i == 0) 
        { 
            factors.Add(i); 
            k /= i; 
        } 
    } 
    if (k > 1) 
        factors.Add(k); 

    // Initialize the count of each 
    // character position as 1 
    int []count = new int[n]; 
    for (i = 0; i < n; i++) 
        count[i] = 1;
    int index = 0; 

    // Loop until the list 
    // becomes empty 
    while (factors.Count > 0) 
    { 

        // Increase the character 
        // count by multiplying it 
        // with the prime factor 
        count[index++] *= factors[factors.Count - 1]; 
        factors.Remove(factors[factors.Count - 1]); 

        // If we reach end then again 
        // start from beginning 
        if (index == n) 
            index = 0; 
    } 

    // Store the output 
    String s = ""; 

    for (i = 0; i < n; i++) 
    { 
        while (count[i]-- > 0) 
        { 
            s += str[i]; 
        } 
    } 

    // Print the String 
    Console.Write(s); 
} 

// Driver code 
public static void Main(String[] args) 
{ 
    // Given String 
    String str = "code"; 

    int k = 20; 

    // Function Call 
    printSubsequenceString(str, k); 
}
} 

// This code is contributed by sapnasingh4991

JavaScript

<script>

// Javascript program for the above approach

// Function that computes the string s
function printSubsequenceString(str, k)
{
    // Length of the given string str
    let n = str.length;
    let i;

    // List that stores all the prime
    // factors of given k
    let factors = new Array();

    // Find the prime factors
    for (let i = 2;
        i <= Math.sqrt(k); i++) {

        while (k % i == 0) {
            factors.push(i);
            k /= i;
        }
    }
    if (k > 1)
        factors.push(k);

    // Initialize the count of each
    // character position as 1
    let count = new Array(n).fill(1);

    let index = 0;

    // Loop until the list
    // becomes empty
    while (factors.length > 0) {

        // Increase the character
        // count by multiplying it
        // with the prime factor
        count[index++] *= factors[factors.length - 1];
        factors.pop();

        // If we reach end then again
        // start from beginning
        if (index == n)
            index = 0;
    }

    // Store the output
    let s = new String();

    for (i = 0; i < n; i++) {
        while (count[i]-- > 0) {
            s += str[i];
        }
    }

    // Print the string
    document.write(s);
}

// Driver code

// Given String
let str = "code";

let k = 20;

// Function Call
printSubsequenceString(str, k);

// This code is contributed by _saurabh_jaiswal

</script>

Output:

cccccoodde

Time Complexity: O(N*log₂(log₂(N)))
Auxiliary Space: O(K)

Count binary Strings that does not contain given String as Subsequence

Ganeshchowdharysadanala

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Construct a string that has exactly K subsequences from given string

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