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📜  计数被4整除的旋转

📅  最后修改于: 2021-04-29 11:57:23             🧑  作者: Mango

给定一个大的正数作为字符串,计算给定数的所有可被4整除的旋转。

例子:

Input: 8
Output: 1

Input: 20
Output: 1
Rotation: 20 is divisible by 4
          02 is not divisible by 4

Input : 13502
Output : 0
No rotation is divisible by 4

Input : 43292816
Output : 5
5 rotations are : 43292816, 16432928, 81643292
                  92816432, 32928164 

对于大数,很难将每个数字进行旋转和除以4。因此,使用了“ 4除数”属性,该属性表示如果将数字的最后2位除以4,则数字可以被4除。实际不旋转数字并检查最后2位数字的可除性,而是我们将连续对(以循环方式)计数为可被4整除的对。

插图:

Consider a number 928160
Its rotations are 928160, 092816, 609281, 160928, 
    816092, 281609.
Now form pairs from the original number 928160
as mentioned in the approach.
Pairs: (9,2), (2,8), (8,1), (1,6), 
         (6,0), (0,9)
We can observe that the 2-digit number formed by the these 
pairs, i.e., 92, 28, 81, 16, 60, 09, are present in the last
2 digits of some rotation.
Thus, checking divisibility of these pairs gives the required
number of rotations. 

Note: A single digit number can directly
be checked for divisibility.

下面是该方法的实现。

C++
// C++ program to count all rotation divisible
// by 4.
#include 
using namespace std;
 
// Returns count of all rotations divisible
// by 4
int countRotations(string n)
{
    int len = n.length();
 
    // For single digit number
    if (len == 1)
    {
        int oneDigit = n.at(0)-'0';
        if (oneDigit%4 == 0)
            return 1;
        return 0;
    }
 
    // At-least 2 digit number (considering all
    // pairs)
    int twoDigit, count = 0;
    for (int i=0; i<(len-1); i++)
    {
        twoDigit = (n.at(i)-'0')*10 + (n.at(i+1)-'0');
        if (twoDigit%4 == 0)
            count++;
    }
 
    // Considering the number formed by the pair of
    // last digit and 1st digit
    twoDigit = (n.at(len-1)-'0')*10 + (n.at(0)-'0');
    if (twoDigit%4 == 0)
        count++;
 
    return count;
}
 
//Driver program
int main()
{
    string n = "4834";
    cout << "Rotations: " << countRotations(n) << endl;
    return 0;
}


Java
// Java program to count
// all rotation divisible
// by 4.
import java.io.*;
 
class GFG {
     
    // Returns count of all
    // rotations divisible
    // by 4
    static int countRotations(String n)
    {
        int len = n.length();
      
        // For single digit number
        if (len == 1)
        {
          int oneDigit = n.charAt(0)-'0';
 
          if (oneDigit % 4 == 0)
              return 1;
 
          return 0;
        }
      
        // At-least 2 digit
        // number (considering all
        // pairs)
        int twoDigit, count = 0;
        for (int i = 0; i < (len-1); i++)
        {
          twoDigit = (n.charAt(i)-'0') * 10 +
                     (n.charAt(i+1)-'0');
 
          if (twoDigit%4 == 0)
              count++;
        }
      
        // Considering the number
        // formed by the pair of
        // last digit and 1st digit
        twoDigit = (n.charAt(len-1)-'0') * 10 +
                   (n.charAt(0)-'0');
 
        if (twoDigit%4 == 0)
            count++;
      
        return count;
    }
      
    //Driver program
    public static void main(String args[])
    {
        String n = "4834";
        System.out.println("Rotations: " +
                          countRotations(n));
    }
}
 
// This code is contributed by Nikita tiwari.


Python3
# Python3 program to count
# all rotation divisible
# by 4.
 
# Returns count of all
# rotations divisible
# by 4
def countRotations(n) :
 
    l = len(n)
 
    # For single digit number
    if (l == 1) :
        oneDigit = (int)(n[0])
         
        if (oneDigit % 4 == 0) :
            return 1
        return 0
     
     
    # At-least 2 digit number
    # (considering all pairs)
    count = 0
    for i in range(0, l - 1) :
        twoDigit = (int)(n[i]) * 10 + (int)(n[i + 1])
         
        if (twoDigit % 4 == 0) :
            count = count + 1
             
    # Considering the number
    # formed by the pair of
    # last digit and 1st digit
    twoDigit = (int)(n[l - 1]) * 10 + (int)(n[0])
    if (twoDigit % 4 == 0) :
        count = count + 1
 
    return count
 
# Driver program
n = "4834"
print("Rotations: " ,
    countRotations(n))
 
# This code is contributed by Nikita tiwari.


C#
// C# program to count all rotation
// divisible by 4.
using System;
 
class GFG {
     
    // Returns count of all
    // rotations divisible
    // by 4
    static int countRotations(String n)
    {
        int len = n.Length;
     
        // For single digit number
        if (len == 1)
        {
            int oneDigit = n[0] - '0';
     
            if (oneDigit % 4 == 0)
                return 1;
     
            return 0;
        }
     
        // At-least 2 digit
        // number (considering all
        // pairs)
        int twoDigit, count = 0;
        for (int i = 0; i < (len - 1); i++)
        {
            twoDigit = (n[i] - '0') * 10 +
                          (n[i + 1] - '0');
     
            if (twoDigit % 4 == 0)
                count++;
        }
     
        // Considering the number
        // formed by the pair of
        // last digit and 1st digit
        twoDigit = (n[len - 1] - '0') * 10 +
                               (n[0] - '0');
 
        if (twoDigit % 4 == 0)
            count++;
     
        return count;
    }
     
    //Driver program
    public static void Main()
    {
        String n = "4834";
        Console.Write("Rotations: " +
                    countRotations(n));
    }
}
 
// This code is contributed by nitin mittal.


PHP


Javascript


输出:

Rotations: 2

时间复杂度: O(n),其中n是输入数字中的位数。