Minimum removals in a number to be divisible by 10 power raised to K

Given two positive integers N and K. Find the minimum number of digits that can be removed from the number N such that after removals the number is divisible by 10K or print -1 if it is impossible.

Examples:

Input : N = 10904025, K = 2
Output : 3
Explanation : We can remove the digits 4, 2 and 5 such that the number 
becomes 10900 which is divisible by 102.

Input : N = 1000, K = 5
Output : 3
Explanation : We can remove the digits 1 and any two zeroes such that the
number becomes 0 which is divisible by 105

Input : N = 23985, K = 2
Output : -1

Approach : The idea is to start traversing the number from the last digit while keeping a counter. If the current digit is not zero, increment the counter variable, otherwise decrement variable K. When K becomes zero, return counter as answer. After traversing the whole number, check if the current value of K is zero or not. If it is zero, return counter as answer, otherwise return answer as number of digits in N – 1, since we need to reduce the whole number to a single zero which is divisible by any number. Also, if the given number does not contain any zero, return -1 as answer.

Below is the implementation of above approach.

C++

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// CPP Program to count the number
// of digits that can be removed such
// that number is divisible by 10^K
#include <bits/stdc++.h>
using namespace std;
  
// function to return the required
// number of digits to be removed
int countDigitsToBeRemoved(int N, int K)
{
    // Converting the given number
    // into string
    string s = to_string(N);
  
    // variable to store number of
    // digits to be removed
    int res = 0;
  
    // variable to denote if atleast
    // one zero has been found
    int f_zero = 0;
    for (int i = s.size() - 1; i >= 0; i--) {
        if (K == 0)
            return res;
        if (s[i] == '0') {
  
            // zero found
            f_zero = 1;
            K--;
        }
        else
            res++;
    }
  
    // return size - 1 if K is not zero and
    // atleast one zero is present, otherwise
    // result
    if (!K)
        return res;
    else if (f_zero)
        return s.size() - 1;
    return -1;
}
  
// Driver Code to test above function
int main()
{
    int N = 10904025, K = 2;
    cout << countDigitsToBeRemoved(N, K) << endl;
  
    N = 1000, K = 5;
    cout << countDigitsToBeRemoved(N, K) << endl;
  
    N = 23985, K = 2;
    cout << countDigitsToBeRemoved(N, K) << endl;
    return 0;
}

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Java

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// Java Program to count the number 
// of digits that can be removed such 
// that number is divisible by 10^K 
  
public class GFG{
      
    // function to return the required 
    // number of digits to be removed 
    static int countDigitsToBeRemoved(int N, int K) 
    
        // Converting the given number 
        // into string 
        String s = Integer.toString(N); 
      
        // variable to store number of 
        // digits to be removed 
        int res = 0
      
        // variable to denote if atleast 
        // one zero has been found 
        int f_zero = 0
        for (int i = s.length() - 1; i >= 0; i--) { 
            if (K == 0
                return res; 
            if (s.charAt(i) == '0') { 
      
                // zero found 
                f_zero = 1
                K--; 
            
            else
                res++; 
        
      
        // return size - 1 if K is not zero and 
        // atleast one zero is present, otherwise 
        // result 
        if (K == 0
            return res; 
        else if (f_zero == 1
            return s.length() - 1
        return -1
    
      
    // Driver Code to test above function 
    public static void main(String []args)
    
        int N = 10904025;
        int K = 2
        System.out.println(countDigitsToBeRemoved(N, K)) ; 
      
        N = 1000 ;
        K = 5
        System.out.println(countDigitsToBeRemoved(N, K))  ;
      
        N = 23985;
        K = 2
        System.out.println(countDigitsToBeRemoved(N, K)) ; 
    
  
    // This code is contributed by Ryuga
    }

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Python3

# Python3 Program to count the number
# of digits that can be removed such
# that number is divisible by 10^K

# function to return the required
# number of digits to be removed
def countDigitsToBeRemoved(N, K):

# Converting the given number
# into string
s = str(N);

# variable to store number of
# digits to be removed
res = 0;

# variable to denote if atleast
# one zero has been found
f_zero = 0;
for i in range(len(s) – 1, -1, -1):
if (K == 0):
return res;
if (s[i] == ‘0’):

# zero found
f_zero = 1;
K -= 1;
else:
res += 1;

# return size – 1 if K is not zero and
# atleast one zero is present, otherwise
# result
if (K == 0):
return res;
elif (f_zero > 0):
return len(s) – 1;
return -1;

# Driver Code
N = 10904025;
K = 2;
print(countDigitsToBeRemoved(N, K));

N = 1000;
K = 5;
print(countDigitsToBeRemoved(N, K));

N = 23985;
K = 2;
print(countDigitsToBeRemoved(N, K));

# This code is contributed by mits

C#

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// C# Program to count the number 
// of digits that can be removed such 
// that number is divisible by 10^K 
   
using System;
public class GFG{
       
    // function to return the required 
    // number of digits to be removed 
    static int countDigitsToBeRemoved(int N, int K) 
    
        // Converting the given number 
        // into string 
        string s = Convert.ToString(N); 
       
        // variable to store number of 
        // digits to be removed 
        int res = 0; 
       
        // variable to denote if atleast 
        // one zero has been found 
        int f_zero = 0; 
        for (int i = s.Length - 1; i >= 0; i--) { 
            if (K == 0) 
                return res; 
            if (s[i] == '0') { 
       
                // zero found 
                f_zero = 1; 
                K--; 
            
            else
                res++; 
        
       
        // return size - 1 if K is not zero and 
        // atleast one zero is present, otherwise 
        // result 
        if (K == 0) 
            return res; 
        else if (f_zero == 1) 
            return s.Length - 1; 
        return -1; 
    
       
    // Driver Code to test above function 
    public static void Main()
    
        int N = 10904025;
        int K = 2; 
        Console.Write(countDigitsToBeRemoved(N, K)+"\n") ; 
       
        N = 1000 ;
        K = 5; 
        Console.Write(countDigitsToBeRemoved(N, K)+"\n")  ;
       
        N = 23985;
        K = 2; 
        Console.Write(countDigitsToBeRemoved(N, K)+"\n") ; 
    
   
     
    }

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PHP

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<?php
// PHP Program to count the number
// of digits that can be removed such
// that number is divisible by 10^K
  
// function to return the required
// number of digits to be removed
function countDigitsToBeRemoved($N, $K)
{
    // Converting the given number
    // into string
    $s = strval($N);
  
    // variable to store number of
    // digits to be removed
    $res = 0;
  
    // variable to denote if atleast
    // one zero has been found
    $f_zero = 0;
    for ($i = strlen($s)-1; $i >= 0; $i--) {
        if ($K == 0)
            return $res;
        if ($s[$i] == '0') {
  
            // zero found
            $f_zero = 1;
            $K--;
        }
        else
            $res++;
    }
  
    // return size - 1 if K is not zero and
    // atleast one zero is present, otherwise
    // result
    if (!$K)
        return $res;
    else if ($f_zero)
        return strlen($s) - 1;
    return -1;
}
  
// Driver Code to test above function
  
    $N = 10904025;
    $K = 2;
    echo countDigitsToBeRemoved($N, $K)."\n";
  
    $N = 1000;
    $K = 5;
    echo countDigitsToBeRemoved($N, $K)."\n";
  
    $N = 23985;
    $K = 2;
    echo countDigitsToBeRemoved($N, $K);
      
// This code is contributed by mits
?>

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Output:

3
3
-1

Time Complexity :Number of digits in the given number.



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