一个数的回文除数

先决条件：找出一个自然数的所有约数
给定一个数字N 。任务是找到N 的所有回文除数。

例子：

Input: N = 66 
Output: 1 2 3 6 11 22 33 66

Input: N = 808 
Output: 1 2 4 8 101 202 404 808
 

方法：

• 使用本文中讨论的方法找到N 的所有除数。
• 对于每个除数 D，检查 D 是否为回文。
• 对所有除数重复上述步骤。

下面是上述方法的实现：

C++14

// C++ program to find all the palindromic
// divisors of a number
#include "bits/stdc++.h"
using namespace std;
 
// Function to check is num is palindromic
// or not
bool isPalindrome(int n)
{
    // Convert n to string str
    string str = to_string(n);
 
    // Starting and ending index of
    // string str
    int s = 0, e = str.length() - 1;
    while (s < e) {
 
        // If char at s and e are
        // not equals then return
        // false
        if (str[s] != str[e]) {
            return false;
        }
        s++;
        e--;
    }
    return true;
}
 
// Function to find  palindromic divisors
void palindromicDivisors(int n)
{
    // To sore the palindromic divisors of
    // number n
    vector PalindromDivisors;
 
    for (int i = 1; i <= sqrt(n); i++) {
 
        // If n is divisible by i
        if (n % i == 0) {
 
            // Check if number is a perfect square
            if (n / i == i) {
 
                // Check divisor is palindromic,
                // then store it
                if (isPalindrome(i)) {
                    PalindromDivisors.push_back(i);
                }
            }
            else {
 
                // Check if divisors are palindrome
                if (isPalindrome(i)) {
                    PalindromDivisors.push_back(i);
                }
 
                // Check if n / divisors is palindromic
                // or not
                if (isPalindrome(n / i)) {
                    PalindromDivisors.push_back(n / i);
                }
            }
        }
    }
 
    // Print all palindromic divisors in sorted order
    sort(PalindromDivisors.begin(),
         PalindromDivisors.end());
 
    for (int i = 0; i < PalindromDivisors.size();
         i++) {
        cout << PalindromDivisors[i] << " ";
    }
}
 
// Driver code
int main()
{
    int n = 66;
 
    // Function call to find all palindromic
    // divisors
    palindromicDivisors(n);
}

Java

// Java program to find all the palindromic
// divisors of a number
import java.util.*;
 
class GFG
{
 
// Function to check is num is palindromic
// or not
static boolean isPalindrome(int n)
{
    // Convert n to String str
    String str = String.valueOf(n);
 
    // Starting and ending index of
    // String str
    int s = 0, e = str.length() - 1;
    while (s < e) {
 
        // If char at s and e are
        // not equals then return
        // false
        if (str.charAt(s) != str.charAt(e)) {
            return false;
        }
        s++;
        e--;
    }
    return true;
}
 
// Function to find palindromic divisors
static void palindromicDivisors(int n)
{
    // To sore the palindromic divisors of
    // number n
    Vector PalindromDivisors = new Vector();
 
    for (int i = 1; i <= Math.sqrt(n); i++) {
 
        // If n is divisible by i
        if (n % i == 0) {
 
            // Check if number is a perfect square
            if (n / i == i) {
 
                // Check divisor is palindromic,
                // then store it
                if (isPalindrome(i)) {
                    PalindromDivisors.add(i);
                }
            }
            else {
 
                // Check if divisors are palindrome
                if (isPalindrome(i)) {
                    PalindromDivisors.add(i);
                }
 
                // Check if n / divisors is palindromic
                // or not
                if (isPalindrome(n / i)) {
                    PalindromDivisors.add(n / i);
                }
            }
        }
    }
 
    // Print all palindromic divisors in sorted order
    Collections.sort(PalindromDivisors);
 
    for (int i = 0; i < PalindromDivisors.size();
        i++) {
        System.out.print(PalindromDivisors.get(i)+ " ");
    }
}
 
// Driver code
public static void main(String[] args)
{
    int n = 66;
 
    // Function call to find all palindromic
    // divisors
    palindromicDivisors(n);
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 program to find all the palindromic
# divisors of a number
from math import sqrt;
 
# Function to check is num is palindromic
# or not
def isPalindrome(n) :
 
    # Convert n to string str
    string = str(n);
 
    # Starting and ending index of
    # string str
    s = 0; e = len(string) - 1;
    while (s < e) :
 
        # If char at s and e are
        # not equals then return
        # false
        if (string[s] != string[e]) :
            return False;
         
        s += 1;
        e -= 1;
     
    return True;
 
# Function to find palindromic divisors
def palindromicDivisors(n) :
 
    # To sore the palindromic divisors of
    # number n
    PalindromDivisors = [];
 
    for i in range(1, int(sqrt(n))) :
 
        # If n is divisible by i
        if (n % i == 0) :
 
            # Check if number is a perfect square
            if (n // i == i) :
 
                # Check divisor is palindromic,
                # then store it
                if (isPalindrome(i)) :
                    PalindromDivisors.append(i);
             
            else :
 
                # Check if divisors are palindrome
                if (isPalindrome(i)) :
                    PalindromDivisors.append(i);
 
                # Check if n / divisors is palindromic
                # or not
                if (isPalindrome(n // i)) :
                    PalindromDivisors.append(n // i);
 
    # Print all palindromic divisors in sorted order
    PalindromDivisors.sort();
     
    for i in range(len( PalindromDivisors)) :
        print(PalindromDivisors[i] ,end=" ");
 
# Driver code
if __name__ == "__main__" :
 
    n = 66;
 
    # Function call to find all palindromic
    # divisors
    palindromicDivisors(n);
 
# This code is contributed by AnkitRai01

C#

// C# program to find all the palindromic
// divisors of a number
using System;
using System.Collections.Generic;
 
class GFG
{
 
// Function to check is num is palindromic
// or not
static bool isPalindrome(int n)
{
    // Convert n to String str
    String str = String.Join("",n);
 
    // Starting and ending index of
    // String str
    int s = 0, e = str.Length - 1;
    while (s < e)
    {
 
        // If char at s and e are
        // not equals then return
        // false
        if (str[s] != str[e])
        {
            return false;
        }
        s++;
        e--;
    }
    return true;
}
 
// Function to find palindromic divisors
static void palindromicDivisors(int n)
{
    // To sore the palindromic divisors of
    // number n
    List PalindromDivisors = new List();
 
    for (int i = 1; i <= Math.Sqrt(n); i++)
    {
 
        // If n is divisible by i
        if (n % i == 0)
        {
 
            // Check if number is a perfect square
            if (n / i == i)
            {
 
                // Check divisor is palindromic,
                // then store it
                if (isPalindrome(i))
                {
                    PalindromDivisors.Add(i);
                }
            }
            else
            {
 
                // Check if divisors are palindrome
                if (isPalindrome(i))
                {
                    PalindromDivisors.Add(i);
                }
 
                // Check if n / divisors is palindromic
                // or not
                if (isPalindrome(n / i))
                {
                    PalindromDivisors.Add(n / i);
                }
            }
        }
    }
 
    // Print all palindromic divisors in sorted order
    PalindromDivisors.Sort();
 
    for (int i = 0; i < PalindromDivisors.Count;
        i++)
    {
        Console.Write(PalindromDivisors[i]+ " ");
    }
}
 
// Driver code
public static void Main(String[] args)
{
    int n = 66;
 
    // Function call to find all palindromic
    // divisors
    palindromicDivisors(n);
}
}
 
// This code is contributed by PrinciRaj1992

Javascript

 
// Javascript program to find all the palindromic
// divisors of a number
 
// Function to check is num is palindromic
// or not
function isPalindrome(n)
{
     
    // Convert n to string str
    var str = (n.toString());
 
    // Starting and ending index of
    // string str
    var s = 0, e = str.length - 1;
     
    while (s < e)
    {
         
        // If char at s and e are
        // not equals then return
        // false
        if (str[s] != str[e])
        {
            return false;
        }
        s++;
        e--;
    }
    return true;
}
 
// Function to find  palindromic divisors
function palindromicDivisors(n)
{
     
    // To sore the palindromic divisors of
    // number n
    var PalindromDivisors = [];
 
    for(var i = 1; i <= parseInt(Math.sqrt(n)); i++)
    {
         
        // If n is divisible by i
        if (n % i == 0)
        {
 
            // Check if number is a perfect square
            if (n / i == i)
            {
 
                // Check divisor is palindromic,
                // then store it
                if (isPalindrome(i))
                {
                    PalindromDivisors.push(i);
                }
            }
            else
            {
                 
                // Check if divisors are palindrome
                if (isPalindrome(i))
                {
                    PalindromDivisors.push(i);
                }
 
                // Check if n / divisors is palindromic
                // or not
                if (isPalindrome(n / i))
                {
                    PalindromDivisors.push(n / i);
                }
            }
        }
    }
 
    // Print all palindromic divisors in sorted order
    PalindromDivisors.sort((a, b) => a - b)
 
    for(var i = 0;
            i < PalindromDivisors.length; i++)
    {
        document.write( PalindromDivisors[i] + " ");
    }
}
 
// Driver code
var n = 66;
 
// Function call to find all palindromic
// divisors
palindromicDivisors(n);
 
// This code is contributed by rrrtnx
 

输出：

1 2 3 6 11 22 33 66

时间复杂度： O(N*log N)

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