检查给定数字是否可折

给定一个整数n，找出n是否为可整除的。在数学中，如果数字遵循某些独特的性质，则该数字称为“可折除的数”。该数字不应包含任何前导零。输入数字的前i个数字组成的数字应可被i整除，其中$i > 1 ~and ~i <= number ~of ~digits ~in ~the ~input ~number$ 。如果遵循这些属性的任何数字，则称为“可折数” 。
例子：

Input: 345654
Output: 345654 is Polydivisible number.
Explanation: 
The first digit of the number is non-zero. 
The number formed by the first 2 digits(34) 
is divisible by 2. The number formed by the
first 3 digits(345) is divisible by 3. 
The number formed by the first 4 digits(3456)
is divisible by 4. The number formed by the
first 5 digits(34565) is divisible by 5. 
The number formed by the first 6 digits(345654)
is divisible by 6.     

Input: 130
Output: 130 is Not Polydivisible number.

Input: 129
Output: 129 is Polydivisible number.    

方法：这个想法很简单。

1. Extract all the digits of the array and store them in an array.
2. Pick first 2 digits and form a number and check if it is divisible by 2.
3. Pick ith digit and append to the existing number and check if the number is divisible by i.
4. If all the above conditions are satisfied until all the digits are exhausted,then the given number is Polydivisible.

下面是上述方法的实现。

C++

// CPP program to check whether
// a number is polydivisible or not
#include 
using namespace std;
  
// function to check polydivisible
// number
void check_polydivisible(int n)
{
    int N = n;
    vector digit;
  
    // digit extraction of input number
    while (n > 0) {
  
        // store the digits in an array
        digit.push_back(n % 10);
        n /= 10;
    }
    reverse(digit.begin(), digit.end());
  
    bool flag = true;
    n = digit[0];
    for (int i = 1; i < digit.size(); i++) {
  
        // n contains first i digits
        n = n * 10 + digit[i];
  
        // n should be divisible by i
        if (n % (i + 1) != 0) {
            flag = false;
            break;
        }
    }
    if (flag)
        cout << N << " is Polydivisible number.";
    else
        cout << N << " is Not Polydivisible number.";
}
  
int main()
{
    int n = 345654;
    check_polydivisible(n);
}

Java

// Java program to check whether
// a number is polydivisible or not
import java.util.*;
import java.io.*;
  
class GFG {
      
    // function to check polydivisible
    // number
    static void check_polydivisible(int n)
    {
        int N = n;
        Vector digit = new Vector();
      
        // digit extraction of input number
        while (n > 0) {
      
            // store the digits in an array
            digit.add(new Integer(n % 10));
            n /= 10;
        }
        Collections.reverse(digit);
      
        boolean flag = true;
        n = digit.get(0);
        for (int i = 1; i < digit.size(); i++) {
      
            // n contains first i digits
            n = n * 10 + digit.get(i);
      
            // n should be divisible by i
            if (n % (i + 1) != 0) {
                flag = false;
                break;
            }
        }
        if (flag)
            System.out.println(N + " is Polydivisible number.");
        else
            System.out.println(N + " is Not Polydivisible number.");
    }
      
    // Driver code
    public static void main (String[] args) 
    {
        int n = 345654;
        check_polydivisible(n);
    }
}

Python3

# Python 3 program to check whether
# a number is polydivisible or not
  
# function to check polydivisible
# number
def check_polydivisible(n):
    N = n
    digit = []
  
    # digit extraction of input number
    while (n > 0):
          
        # store the digits in an array
        digit.append(n % 10)
        n /= 10
  
    digit.reverse()
  
    flag = True
    n = digit[0]
    for i in range(1, len(digit), 1):
          
        # n contains first i digits
        n = n * 10 + digit[i]
  
        # n should be divisible by i
        if (n % (i + 1) != 0):
            flag = False
            break
      
    if (flag):
        print(N, "is Polydivisible number.");
    else:
        print(N, "is Not Polydivisible number.")
  
# Driver Code
if __name__ == '__main__':
    n = 345654
    check_polydivisible(n)
  
      
# This code is contributed by
# Sahil_Shelangia

C#

// C# program to check whether
// a number is polydivisible or not
using System;
using System.Collections.Generic;
  
class GFG 
{
      
    // function to check polydivisible
    // number
    static void check_polydivisible(int n)
    {
        int N = n;
        List digit = new List();
      
        // digit extraction of input number
        while (n > 0) 
        {
      
            // store the digits in an array
            digit.Add((int)n % 10);
            n /= 10;
        }
        digit.Reverse();
      
        bool flag = true;
        n = digit[0];
        for (int i = 1; i < digit.Count; i++) 
        {
      
            // n contains first i digits
            n = n * 10 + digit[i];
      
            // n should be divisible by i
            if (n % (i + 1) != 0)
            {
                flag = false;
                break;
            }
        }
        if (flag)
            Console.WriteLine(N + 
                    " is Polydivisible number.");
        else
            Console.WriteLine(N + 
                    " is Not Polydivisible number.");
    }
      
    // Driver code
    public static void Main (String[] args) 
    {
        int n = 345654;
        check_polydivisible(n);
    }
}
  
// This code is contributed by Rajput-Ji

输出：

345654 is Polydivisible number.