回文自拍号
原文:https://www.geeksforgeeks.org/palindromic-selfie-numbers/
给定一个数 x，根据自拍乘法法则找到它的回文自拍数。如果不存在这样的号码，则打印“不存在这样的号码”。 回文自拍号满足自拍乘法规则，使得存在另一个编号 y，编号 y 的x * reverse _ digits _ of(x)= y * reverse _ digits _ of(y)，条件是编号 y 是通过对 x 中的数字进行某种排序得到的，即 x 和 y 应该具有相同的数字，但顺序不同。 示例:
Input : 1224
Output : 2142
Explanation :
Because, 1224 X 4221 = 2142 X 2412
And all digits of 2142 are formed by a different
permutation of the digits in 1224
(Note: The valid output is either be 2142 or 2412)
Input : 13452
Output : 14532
Explanation :
Because, 13452 X 25431 = 14532 X 23541
And all digits of 14532 are formed by a different
permutation of the digits in 13452
Input : 12345
Output : No such number exists
Explanation :
Because, with no combination of digits 1, 2, 3, 4, 5
could we get a number that satisfies
12345 X 54321 = number X reverse_of_its_digits
进场:
- 其思想是分解数字，获得数字中数字的所有排列。
- 然后，从获得的排列集合中移除数字及其回文，这将形成我们等式的 LHS。
- 为了检查 RHS，我们现在迭代所有其他置换等式
LHS = current_number X palindrome(current_number)
- 一旦我们得到匹配，我们就以肯定的消息退出循环，否则打印“没有这样的号码可用”。
以下是上述方法的实施:
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find palindromic selfie numbers
import java.util.*;
public class palindrome_selfie {
// To store all permutations of digits in the number
Set<Integer> all_permutes = new HashSet<Integer>();
int number; // input number
public palindrome_selfie(int num)
{
number = num;
}
// Function to reverse the digits of a number
public int palindrome(int num)
{
int reversednum = 0;
int d;
while (num > 0) {
d = num % 10; // Extract last digit
// Append it at the beg
reversednum = reversednum * 10 + d;
num = num / 10; // Reduce number until 0
}
return reversednum;
}
// Function to check palindromic selfie
public void palin_selfie()
{
// Length of the number required for
// calculating all permutations of the digits
int l = String.valueOf(number).length() - 1;
this.permute(number, 0, l); // Calculate all permutations
/* Remove the number and its palindrome from
the obtained set as this is the LHS of
multiplicative equality */
all_permutes.remove(palindrome(number));
all_permutes.remove(number);
boolean flag = false; // Denotes the status result
// Iterate over all other numbers
Iterator it = all_permutes.iterator();
while (it.hasNext()) {
int number2 = (int)it.next();
// Check for equality x*palin(x) = y*palin(y)
if (number * palindrome(number) ==
number2 * palindrome(number2)) {
System.out.println("Palindrome multiplicative" +
"selfie of "+ number + " is : "
+ number2);
flag = true; // Answer found
break;
}
}
// If no such number found
if (flag == false) {
System.out.println("Given number has no palindrome selfie.");
}
}
// Function to get all possible possible permutations
// of the digits in num
public void permute(int num, int l, int r)
{
// Adds the new permutation obtained in the set
if (l == r)
all_permutes.add(num);
else {
for (int i = l; i <= r; i++) {
// Swap digits to get a different ordering
num = swap(num, l, i);
// Recurse to next pair of digits
permute(num, l + 1, r);
num = swap(num, l, i); // Swap back
}
}
}
// Function that swaps the digits i and j in the num
public int swap(int num, int i, int j)
{
char temp;
// Convert int to char array
char[] charArray = String.valueOf(num).toCharArray();
// Swap the ith and jth character
temp = charArray[i];
charArray[i] = charArray[j];
charArray[j] = temp;
// Convert back to int and return
return Integer.valueOf(String.valueOf(charArray));
}
// Driver Function
public static void main(String args[])
{
// First example, input = 145572
palindrome_selfie example1 = new palindrome_selfie(145572);
example1.palin_selfie();
// Second example, input = 19362
palindrome_selfie example2 = new palindrome_selfie(19362);
example2.palin_selfie();
// Third example, input = 4669
palindrome_selfie example3 = new palindrome_selfie(4669);
example3.palin_selfie();
}
}
C
// C# program to find palindromic selfie numbers
using System;
using System.Collections.Generic;
public class palindrome_selfie
{
// To store all permutations of digits in the number
HashSet<int> all_permutes = new HashSet<int>();
int number; // input number
public palindrome_selfie(int num)
{
number = num;
}
// Function to reverse the digits of a number
public int palindrome(int num)
{
int reversednum = 0;
int d;
while (num > 0)
{
d = num % 10; // Extract last digit
// Append it at the beg
reversednum = reversednum * 10 + d;
num = num / 10; // Reduce number until 0
}
return reversednum;
}
// Function to check palindromic selfie
public void palin_selfie()
{
// Length of the number required for
// calculating all permutations of the digits
int l = String.Join("",number).Length - 1;
this.permute(number, 0, l); // Calculate all permutations
/* Remove the number and its palindrome from
the obtained set as this is the LHS of
multiplicative equality */
all_permutes.Remove(palindrome(number));
all_permutes.Remove(number);
bool flag = false; // Denotes the status result
// Iterate over all other numbers
foreach (var number2 in all_permutes)
{
// Check for equality x*palin(x) = y*palin(y)
if (number * palindrome(number) ==
number2 * palindrome(number2))
{
Console.WriteLine("Palindrome multiplicative" +
"selfie of "+ number + " is : "
+ number2);
flag = true; // Answer found
break;
}
}
// If no such number found
if (flag == false)
{
Console.WriteLine("Given number has "+
"no palindrome selfie.");
}
}
// Function to get all possible possible
// permutations of the digits in num
public void permute(int num, int l, int r)
{
// Adds the new permutation obtained in the set
if (l == r)
all_permutes.Add(num);
else
{
for (int i = l; i <= r; i++)
{
// Swap digits to get a different ordering
num = swap(num, l, i);
// Recurse to next pair of digits
permute(num, l + 1, r);
num = swap(num, l, i); // Swap back
}
}
}
// Function that swaps the
// digits i and j in the num
public int swap(int num, int i, int j)
{
char temp;
// Convert int to char array
char[] charArray = String.Join("",num).ToCharArray();
// Swap the ith and jth character
temp = charArray[i];
charArray[i] = charArray[j];
charArray[j] = temp;
// Convert back to int and return
return int.Parse(String.Join("",charArray));
}
// Driver code
public static void Main(String []args)
{
// First example, input = 145572
palindrome_selfie example1 = new palindrome_selfie(145572);
example1.palin_selfie();
// Second example, input = 19362
palindrome_selfie example2 = new palindrome_selfie(19362);
example2.palin_selfie();
// Third example, input = 4669
palindrome_selfie example3 = new palindrome_selfie(4669);
example3.palin_selfie();
}
}
// This code contributed by Rajput-Ji
输出:
Palindrome multiplicative selfie of 145572 is : 157452
Given number has no palindrome selfie.
Palindrome multiplicative selfie of 4669 is : 6496
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