Split the number N by maximizing the count of subparts divisible by K

Last Updated : 18 Feb, 2022

Given a numeric string N and an integer K, the task is to split digits of N into subparts such that the number of segments divisible by K is maximized.
Note: We can make any number of vertical cuts between pairs of adjacent digits.

Examples:

Input: N = 32, K = 4
Output: 1
Explanation:
32 is divisible by 4 but none if its digits are individually divisible, so we don’t perform any splits.
Input: N = 2050, K = 5
Output: 3
Explanation:
2050 can be split into 2, 0, 5, 0 where 0, 5, 0 are divisible by 5.
Input: N = 00001242, K = 3
Output: 6
Explanation:
00001242 can be split into 0, 0, 0, 0, 12, 42 where all the parts are divisible by 3.

Approach:
To solve the problem mentioned above we will try to use a recursive approach.

Check if there is a vertical partition between the current character and the next one, if no then we perform recursion again for the next index and update the substring value by concatenating the present character.
Now, if there is a vertical partition between the current character and the next character, then there exist two cases:
1. If the present subStr is divisible by X, then we add 1 because the present subStr is 1 of the possible answer, then recur for the next index and update subStr as an empty string.
2. If the present subStr is not divisible by X, then we simply recur for the next index and update subStr as an empty string.
Return a maximum of the two possible cases mentioned above.

Below is the implementation of the above logic

C++

// C++ program to split the number N
// by maximizing the count
// of subparts divisible by K
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to count the subparts
int count(string N, int X,
          string subStr,
          int index, int n)
{
 
    if (index == n)
        return 0;
 
    // Total subStr till now
    string a = subStr + N[index];
 
    // b marks the subString up till now
    // is divisible by X or not,
 
    // If it can be divided,
    // then this substring is one
    // of the possible answer
    int b = 0;
 
    // Convert string to long long and
    // check if its divisible with X
    if (stoll(a) % X == 0)
        b = 1;
 
    // Consider there is no vertical
    // cut between this index and the
    // next one, hence take total
    // carrying total substr a.
    int m1 = count(N, X, a, index + 1, n);
 
    // If there is vertical
    // cut between this index
    // and next one, then we
    // start again with subStr as ""
    // and add b for the count
    // of subStr upto now
    int m2 = b + count(N, X, "",
                       index + 1, n);
 
    // Return max of both the cases
    return max(m1, m2);
}
 
// Driver code
int main()
{
    string N = "00001242";
 
    int K = 3;
 
    int l = N.length();
 
    cout << count(N, K, "", 0, l)
         << endl;
 
    return 0;
}

Java

// Java program to split the number N
// by maximizing the count
// of subparts divisible by K
class GFG{
 
// Function to count the subparts
static int count(String N, int X,
                 String subStr,
                 int index, int n)
{
    if (index == n)
        return 0;
 
    // Total subStr till now
    String a = subStr + N.charAt(index);
 
    // b marks the subString up till now
    // is divisible by X or not,
 
    // If it can be divided,
    // then this subString is one
    // of the possible answer
    int b = 0;
 
    // Convert String to long and
    // check if its divisible with X
    if (Long.valueOf(a) % X == 0)
        b = 1;
 
    // Consider there is no vertical
    // cut between this index and the
    // next one, hence take total
    // carrying total substr a.
    int m1 = count(N, X, a, index + 1, n);
 
    // If there is vertical
    // cut between this index
    // and next one, then we
    // start again with subStr as ""
    // and add b for the count
    // of subStr upto now
    int m2 = b + count(N, X, "",
                       index + 1, n);
 
    // Return max of both the cases
    return Math.max(m1, m2);
}
 
// Driver code
public static void main(String[] args)
{
    String N = "00001242";
 
    int K = 3;
 
    int l = N.length();
 
    System.out.print(count(N, K, "", 0, l) + "\n");
}
}
 
// This code is contributed by Rajput-Ji

Python3

# Python3 program to split the number N
# by maximizing the count
# of subparts divisible by K
 
# Function to count the subparts
def count(N, X, subStr, index, n):
     
    if (index == n):
        return 0
     
    # Total subStr till now
    a = subStr + N[index]
     
    # b marks the subString up till now
    # is divisible by X or not,
 
    # If it can be divided,
    # then this substring is one
    # of the possible answer
    b = 0
 
    # Convert string to long long and
    # check if its divisible with X
    if (int(a) % X == 0):
        b = 1
     
    # Consider there is no vertical
    # cut between this index and the
    # next one, hence take total
    # carrying total substr a.
    m1 = count(N, X, a, index + 1, n)
 
    # If there is vertical
    # cut between this index
    # and next one, then we
    # start again with subStr as ""
    # and add b for the count
    # of subStr upto now
    m2 = b + count(N, X, "", index + 1, n)
 
    # Return max of both the cases
    return max(m1, m2) 
     
# Driver code
N = "00001242"
K = 3
 
l = len(N)
 
print(count(N, K, "", 0, l))
 
# This code is contributed by sanjoy_62 

C#

// C# program to split the number N
// by maximizing the count
// of subparts divisible by K
using System;
class GFG{
 
// Function to count the subparts
static int count(String N, int X,
                 String subStr,
                 int index, int n)
{
    if (index == n)
        return 0;
 
    // Total subStr till now
    String a = subStr + N[index];
 
    // b marks the subString up till now
    // is divisible by X or not,
 
    // If it can be divided,
    // then this subString is one
    // of the possible answer
    int b = 0;
 
    // Convert String to long and
    // check if its divisible with X
    if (long. Parse(a) % X == 0)
        b = 1;
 
    // Consider there is no vertical
    // cut between this index and the
    // next one, hence take total
    // carrying total substr a.
    int m1 = count(N, X, a, index + 1, n);
 
    // If there is vertical
    // cut between this index
    // and next one, then we
    // start again with subStr as ""
    // and add b for the count
    // of subStr upto now
    int m2 = b + count(N, X, "",
                  index + 1, n);
 
    // Return max of both the cases
    return Math.Max(m1, m2);
}
 
// Driver code
public static void Main(String[] args)
{
    String N = "00001242";
 
    int K = 3;
 
    int l = N.Length;
 
    Console.Write(count(N, K, "", 0, l) + "\n");
}
}
 
// This code is contributed by Rajput-Ji

Javascript

<script>
 
// Javascript program to split the number N
// by maximizing the count
// of subparts divisible by K
 
// Function to count the subparts
function count(N, X,
                 subStr,
                 index, n)
{
    if (index == n)
        return 0;
   
    // Total subStr till now
    let a = subStr + N[index];
   
    // b marks the subString up till now
    // is divisible by X or not,
   
    // If it can be divided,
    // then this subString is one
    // of the possible answer
    let b = 0;
   
    // Convert String to long and
    // check if its divisible with X
    if (parseInt(a) % X == 0)
        b = 1;
   
    // Consider there is no vertical
    // cut between this index and the
    // next one, hence take total
    // carrying total substr a.
    let m1 = count(N, X, a, index + 1, n);
   
    // If there is vertical
    // cut between this index
    // and next one, then we
    // start again with subStr as ""
    // and add b for the count
    // of subStr upto now
    let m2 = b + count(N, X, "",
                       index + 1, n);
   
    // Return max of both the cases
    return Math.max(m1, m2);
}
 
// Driver Code
     
    let N = "00001242";
   
    let K = 3;
   
    let l = N.length;
   
    document.write(count(N, K, "", 0, l) + "\n");
     
</script>