Minimum number of swaps required to make a number divisible by 60

Given an integer N , the task is to find the minimum number of swaps required to make N divisible by 60. If not possible, then print “-1“.

Examples:

Input: N = 603
Output: 2
Explanation:
Two swap operations are required:
In the first swap (0, 3): 630
In the second swap (6, 3): 360
Now 360 is divisible by 60.
Therefore the minimum two swaps are required.

Input: N = 205
Output: -1

Approach:



  1. For a number to be divisible by 60, it must be divisible by 2, 3 and 10. Therefore:
    • If the sum of digits of number is not divisible by 3, or
    • If there is no digits which is divisible by 2, or
    • If the number does not contain any 0,

    No swap can make the number divisible by 60. Hence -1 swaps will be required in this case.

  2. Then the minimum number of swaps required can be determined by following rules:
    • If the number is already is divisible by 60, then 0 swaps are required. This can be determined if last digit (LSB) is 0 and the second last digit is divisible by 2.
    • If either of the below cases is true, then 1 swap is required.
      • If last digit (LSB) is 0 and the second last digit is not divisible by 2, or, last digit (LSB) is divisible by 2 and the second last digit is 0.
      • If last digit (LSB) is 0 and the second last digit is not divisible by 2, and there are more than 1 zeroes present in the number.
    • Otherwise 2 swaps required

Below is the implementation of the above approach

CPP

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// C++ program to find minimum number
// of swap operations required
#include <bits/stdc++.h>
using namespace std;
  
// Function that print minimum number
// of swap operations required
void MinimumSwapOperations(string s)
{
    bool zero_exist = false;
    bool multiple_of_2 = false;
    int sum = 0;
    int index_of_zero;
    bool more_zero = false;
  
    for (int i = 0; i < s.length(); i++) {
        int val = s[i] - '0';
  
        // Condition if more than one
        // zero exist
        if (zero_exist == true)
            more_zero = true;
  
        // Condition if zero_exist
        if (val == 0) {
            zero_exist = true;
            index_of_zero = i;
        }
  
        // Computing total sum of all digits
        sum += val;
    }
  
    // Condition if zero does not exist or
    // the sum is not divisible by 3
    if (zero_exist == false || sum % 3 != 0) {
        cout << "-1"
             << "\n";
        return;
    }
  
    for (int i = 0; i < s.length(); i++) {
        int val = s[i] - '0';
  
        // Condition to find a digit that is
        // multiple of 2 other than one zero
        if (val % 2 == 0 && i != index_of_zero)
            multiple_of_2 = true;
    }
  
    // Condition if multiple of 2
    // do not exist
    if (multiple_of_2 == false) {
        cout << "-1"
             << "\n";
        return;
    }
  
    int last_val = s[s.length() - 1] - '0';
    int second_last_val = s[s.length() - 2]
                          - '0';
  
    // Condition for zero swaps
    // means the number is already
    // is divisible by 60
    if (last_val == 0
        && second_last_val % 2 == 0)
        cout << 0 << "\n";
  
    // Condition for only one swap
    else if ((last_val == 0
              && second_last_val % 2 != 0)
             || (last_val % 2 == 0
                 && second_last_val == 0))
        cout << 1 << "\n";
  
    else if (more_zero == true
             && (last_val == 0
                 && second_last_val % 2 != 0))
        cout << 1 << "\n";
  
    // Otherwise 2 swaps required
    else
        cout << 2 << "\n";
}
  
// Driver Code
int main()
{
    string N = "20";
  
    MinimumSwapOperations(N);
  
    return 0;
}

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Java














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// Java program to find minimum number 


// of swap operations required 


class GFG { 


      


    // Function that print minimum number 


    // of swap operations required 


    static void MinimumSwapOperations(String s) 


    { 


        boolean zero_exist = false; 


        boolean multiple_of_2 = false; 


        int sum = 0; 


        int index_of_zero = 0; 


        boolean more_zero = false; 


      


        for (int i = 0; i < s.length(); i++) { 


            int val = s.charAt(i) - '0'; 


      


            // Condition if more than one 


            // zero exist 


            if (zero_exist == true) 


                more_zero = true; 


      


            // Condition if zero_exist 


            if (val == 0) { 


                zero_exist = true; 


                index_of_zero = i; 


            } 


      


            // Computing total sum of all digits 


            sum += val; 


        } 


      


        // Condition if zero does not exist or 


        // the sum is not divisible by 3 


        if (zero_exist == false || sum % 3 != 0) { 


            System.out.println("-1"); 


            return; 


        } 


      


        for (int i = 0; i < s.length(); i++) { 


            int val = s.charAt(i) - '0'; 


      


            // Condition to find a digit that is 


            // multiple of 2 other than one zero 


            if (val % 2 == 0 && i != index_of_zero) 


                multiple_of_2 = true; 


        } 


      


        // Condition if multiple of 2 


        // do not exist 


        if (multiple_of_2 == false) { 


            System.out.println("-1"); 


            return; 


        } 


      


        int last_val = s.charAt(s.length() - 1)- '0'; 


        int second_last_val = s.charAt(s.length() - 2)- '0'; 


      


        // Condition for zero swaps 


        // means the number is already 


        // is divisible by 60 


        if (last_val == 0&& second_last_val % 2 == 0) 


            System.out.println(0); 


      


        // Condition for only one swap 


        else if ((last_val == 0


                  && second_last_val % 2 != 0) 


                 || (last_val % 2 == 0


                     && second_last_val == 0)) 


            System.out.println(1); 


      


        else if (more_zero == true


                 && (last_val == 0


                     && second_last_val % 2 != 0)) 


            System.out.println(1) ; 


      


        // Otherwise 2 swaps required 


        else


            System.out.println(2) ; 


    } 


      


    // Driver Code 


    public static void main (String[] args) 


    { 


        String N = "20"; 


      


        MinimumSwapOperations(N); 


      


    } 


} 


  


// This code is contributed by AnkitRai01 



















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Python3














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# Python3 program to find minimum number 


# of swap operations required 


  


# Function that prminimum number 


# of swap operations required 


def MinimumSwapOperations(s): 


    zero_exist = False


    multiple_of_2 = False


    sum = 0


    index_of_zero = 0


    more_zero = False


  


    for i in range(len(s)): 


        val = ord(s[i]) - ord('0') 


  


        # Condition if more than one 


        # zero exist 


        if (zero_exist == True): 


            more_zero = True


  


        # Condition if zero_exist 


        if (val == 0): 


            zero_exist = True


            index_of_zero = i 


  


        # Computing total sum of all digits 


        sum += val 


  


    # Condition if zero does not exist or 


    # the sum is not divisible by 3 


    if (zero_exist == False or sum % 3 != 0): 


        print("-1") 


        return


  


    for i in range(len(s)): 


        val = ord(s[i]) - ord('0') 


  


        # Condition to find a digit that is 


        # multiple of 2 other than one zero 


        if (val % 2 == 0 and i != index_of_zero): 


            multiple_of_2 = True


  


    # Condition if multiple of 2 


    # do not exist 


    if (multiple_of_2 == False): 


        print("-1") 


        return


  


    last_val = ord(s[len(s) - 1]) - ord('0') 


    second_last_val = ord(s[len(s) - 2])- ord('0') 


  


    # Condition for zero swaps 


    # means the number is already 


    # is divisible by 60 


    if (last_val == 0


        and second_last_val % 2 == 0): 


        print(0) 


  


    # Condition for only one swap 


    elif ((last_val == 0


            and second_last_val % 2 != 0) 


            or (last_val % 2 == 0


                and second_last_val == 0)): 


        print(1) 


  


    elif (more_zero == True


            and (last_val == 0


                and second_last_val % 2 != 0)): 


        print(1) 


  


    # Otherwise 2 swaps required 


    else: 


        print(2) 


  


# Driver Code 


if __name__ == '__main__': 


    N = "20"


  


    MinimumSwapOperations(N) 


  


# This code is contributed by mohit kumar 29 



















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C#














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// C# program to find minimum number 


// of swap operations required 


using System; 


  


class GFG { 


      


    // Function that print minimum number 


    // of swap operations required 


    static void MinimumSwapOperations(string s) 


    { 


        bool zero_exist = false; 


        bool multiple_of_2 = false; 


        int sum = 0; 


        int index_of_zero = 0; 


        bool more_zero = false; 


      


        for (int i = 0; i < s.Length; i++) { 


            int val = s[i] - '0'; 


      


            // Condition if more than one 


            // zero exist 


            if (zero_exist == true) 


                more_zero = true; 


      


            // Condition if zero_exist 


            if (val == 0) { 


                zero_exist = true; 


                index_of_zero = i; 


            } 


      


            // Computing total sum of all digits 


            sum += val; 


        } 


      


        // Condition if zero does not exist or 


        // the sum is not divisible by 3 


        if (zero_exist == false || sum % 3 != 0) { 


            Console.WriteLine("-1"); 


            return; 


        } 


      


        for (int i = 0; i < s.Length; i++) { 


            int val = s[i] - '0'; 


      


            // Condition to find a digit that is 


            // multiple of 2 other than one zero 


            if (val % 2 == 0 && i != index_of_zero) 


                multiple_of_2 = true; 


        } 


      


        // Condition if multiple of 2 


        // do not exist 


        if (multiple_of_2 == false) { 


            Console.WriteLine("-1"); 


            return; 


        } 


      


        int last_val = s[(s.Length - 1)- '0']; 


        int second_last_val = s[(s.Length - 2)- '0']; 


      


        // Condition for zero swaps 


        // means the number is already 


        // is divisible by 60 


        if (last_val == 0&& second_last_val % 2 == 0) 


           Console.WriteLine(0); 


      


        // Condition for only one swap 


        else if ((last_val == 0 


                  && second_last_val % 2 != 0) 


                 || (last_val % 2 == 0 


                     && second_last_val == 0)) 


           Console.WriteLine(1); 


      


        else if (more_zero == true


                 && (last_val == 0 


                     && second_last_val % 2 != 0)) 


            Console.WriteLine(1) ; 


      


        // Otherwise 2 swaps required 


        else


            Console.WriteLine(2) ; 


    } 


      


    // Driver Code 


    public static void Main (string[] args) 


    { 


        string N = "20"; 


      


        MinimumSwapOperations(N); 


      


    } 


} 


  


// This code is contributed by AnkitRai01 



















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Output:


-1





Time complexity: O(N)


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