Longest Subsequence from a numeric String divisible by K

Given an integer K and a numeric string str, the task is to find the longest subsequence from the given string which is divisible by K.

Examples:

Input: str = “121400”, K = 8

Output: 121400

Explanation:

Since the whole string is divisible by 8, the entire string is the answer.

Input: str: “7675437”, K = 64

Output: 64

Explanation:

The longest subsequence from the string which is divisible by 64, is “64” itself.

Approach: The idea is to find all subsequences of the given string and for each subsequence, check if its integer representation is divisible by K or not. Follow the steps below to solve the problem:

Traverse the string. For every character encountered, two possibilities exists.

Either consider the current character in the subsequence or not. For both the cases, proceed to the next characters of the string and find the longest subsequence that is divisible by K.

Compare the longest subsequences obtained above with the current maximum length of longest subsequence and update accordingly.

Repeat the above steps for every character of the string and finally, print the maximum length obtained.

Below is the implementation of the above approach.

// C++ program for the above approach 

#include <bits/stdc++.h> 

using namespace std; 

  

// Function to if the integer representation 

// of the current string is divisible by K 

bool isdivisible(string& newstr, long long K) 

{ 

    // Stores the integer 

    // representation of the string 

    long long num = 0; 

  

    for (int i = 0; i < newstr.size(); i++) { 

        num = num * 10 + newstr[i] - '0'; 

    } 

  

    // Check if the num is 

    // divisible by K 

    if (num % K == 0) 

        return true; 

  

    else

        return false; 

} 

  

// Function to find the longest subsequence 

// which is divisible by K 

void findLargestNo(string& str, string& newstr, 

                   string& ans, int index, 

                   long long K) 

{ 

  

    if (index == (int)str.length()) { 

  

        // If the number is divisible by K 

        if (isdivisible(newstr, K)) { 

  

            // If current number is the 

            // maximum obtained so far 

            if ((ans < newstr 

                 && ans.length() == newstr.length()) 

                || newstr.length() > ans.length()) { 

                ans = newstr; 

            } 

        } 

  

        return; 

    } 

  

    string x = newstr + str[index]; 

  

    // Include the digit at current index 

    findLargestNo(str, x, ans, index + 1, K); 

  

    // Exclude the digit at current index 

    findLargestNo(str, newstr, ans, index + 1, K); 

} 

  

// Driver Code 

int main() 

{ 

  

    string str = "121400"; 

  

    string ans = "", newstr = ""; 

  

    long long K = 8; 

  

    findLargestNo(str, newstr, ans, 0, K); 

  

    // Printing the largest number 

    // which is divisible by K 

    if (ans != "") 

        cout << ans << endl; 

  

    // If no number is found 

    // to be divisible by K 

    else

        cout << -1 << endl; 

}

Output:

121400

Time Complexity: O(N * 2N)

Auxiliary Space: O(1)