回文素数
一个回文素数(有时称为一个触须)是一个素数，也是一个回文数。 给定一个数字 n，打印所有小于或等于 n 的回文素数，例如 n 为 10，输出应为“2，3，5，7′。如果 n 是 20，输出应该是“2，3，5，7，11”。 思路是生成所有小于等于给定数 n 的素数，并检查每个素数是否回文。 使用的方法
以下是上述算法的实现:
C++
// C++ Program to print all palindromic primes
// smaller than or equal to n.
#include<bits/stdc++.h>
using namespace std;
// A function that returns true only if num
// contains one digit
int oneDigit(int num)
{
// comparison operation is faster than
// division operation. So using following
// instead of "return num / 10 == 0;"
return (num >= 0 && num < 10);
}
// A recursive function to find out whether
// num is palindrome or not. Initially, dupNum
// contains address of a copy of num.
bool isPalUtil(int num, int* dupNum)
{
// Base case (needed for recursion termination):
// This statement/ mainly compares the first
// digit with the last digit
if (oneDigit(num))
return (num == (*dupNum) % 10);
// This is the key line in this method. Note
// that all recursive/ calls have a separate
// copy of num, but they all share same copy
// of *dupNum. We divide num while moving up
// the recursion tree
if (!isPalUtil(num/10, dupNum))
return false;
// The following statements are executed when
// we move up the recursion call tree
*dupNum /= 10;
// At this point, if num%10 contains i'th
// digit from beginning, then (*dupNum)%10
// contains i'th digit from end
return (num % 10 == (*dupNum) % 10);
}
// The main function that uses recursive function
// isPalUtil() to find out whether num is palindrome
// or not
int isPal(int num)
{
// If num is negative, make it positive
if (num < 0)
num = -num;
// Create a separate copy of num, so that
// modifications made to address dupNum don't
// change the input number.
int *dupNum = new int(num); // *dupNum = num
return isPalUtil(num, dupNum);
}
// Function to generate all primes and checking
// whether number is palindromic or not
void printPalPrimesLessThanN(int n)
{
// Create a boolean array "prime[0..n]" and
// initialize all entries it as true. A value
// in prime[i] will finally be false if i is
// Not a prime, else true.
bool prime[n+1];
memset(prime, true, sizeof(prime));
for (int p=2; p*p<=n; p++)
{
// If prime[p] is not changed, then it is
// a prime
if (prime[p] == true)
{
// Update all multiples of p
for (int i=p*2; i<=n; i += p)
prime[i] = false;
}
}
// Print all palindromic prime numbers
for (int p=2; p<=n; p++)
// checking whether the given number is
// prime palindromic or not
if (prime[p] && isPal(p))
cout << p << " ";
}
// Driver Program
int main()
{
int n = 100;
printf("Palindromic primes smaller than or "
"equal to %d are :\n", n);
printPalPrimesLessThanN(n);
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to print all palindromic primes
// smaller than or equal to n.
import java.util.*;
class GFG {
// A function that returns true only if num
// contains one digit
static boolean oneDigit(int num)
{
// comparison operation is faster than
// division operation. So using following
// instead of "return num / 10 == 0;"
return (num >= 0 && num < 10);
}
// A recursive function to find out whether
// num is palindrome or not. Initially, dupNum
// contains address of a copy of num.
static boolean isPalUtil(int num, int dupNum)
{
// Base case (needed for recursion termination):
// This statement/ mainly compares the first
// digit with the last digit
if (oneDigit(num))
return (num == (dupNum) % 10);
// This is the key line in this method. Note
// that all recursive/ calls have a separate
// copy of num, but they all share same copy
// of dupNum. We divide num while moving up
// the recursion tree
if (!isPalUtil(num/10, dupNum))
return false;
// The following statements are executed when
// we move up the recursion call tree
dupNum /= 10;
// At this point, if num%10 contains ith
// digit from beginning, then (dupNum)%10
// contains ith digit from end
return (num % 10 == (dupNum) % 10);
}
// The main function that uses recursive function
// isPalUtil() to find out whether num is palindrome
// or not
static boolean isPal(int num)
{
// If num is negative, make it positive
if (num < 0)
num = -num;
// Create a separate copy of num, so that
// modifications made to address dupNum don't
// change the input number.
int dupNum = num; // dupNum = num
return isPalUtil(num, dupNum);
}
// Function to generate all primes and checking
// whether number is palindromic or not
static void printPalPrimesLessThanN(int n)
{
// Create a boolean array "prime[0..n]" and
// initialize all entries it as true. A value
// in prime[i] will finally be false if i is
// Not a prime, else true.
boolean prime[] = new boolean[n+1];
Arrays.fill(prime, true);
for (int p = 2; p*p <= n; p++)
{
// If prime[p] is not changed, then it is
// a prime
if (prime[p])
{
// Update all multiples of p
for (int i = p*2; i <= n; i += p){
prime[i] = false;}
}
}
// Print all palindromic prime numbers
for (int p = 2; p <= n; p++){
// checking whether the given number is
// prime palindromic or not
if (prime[p] && isPal(p)){
System.out.print(p + " ");
}
}
}
// Driver function
public static void main(String[] args)
{
int n = 100;
System.out.printf("Palindromic primes smaller than or "
+"equal to %d are :\n", n);
printPalPrimesLessThanN(n);
}
}
// This code is contributed by Arnav Kr. Mandal.
Python 3
# Python3 Program to print all palindromic
# primes smaller than or equal to n.
# A function that returns true only if
# num contains one digit
def oneDigit(num):
# comparison operation is faster than
# division operation. So using following
# instead of "return num / 10 == 0;"
return (num >= 0 and num < 10);
# A recursive function to find out whether
# num is palindrome or not. Initially, dupNum
# contains address of a copy of num.
def isPalUtil(num, dupNum):
# Base case (needed for recursion termination):
# This statement/ mainly compares the first
# digit with the last digit
if (oneDigit(num)):
return (num == (dupNum) % 10);
# This is the key line in this method. Note
# that all recursive/ calls have a separate
# copy of num, but they all share same copy
# of dupNum. We divide num while moving up
# the recursion tree
if (not isPalUtil(int(num / 10), dupNum)):
return False;
# The following statements are executed
# when we move up the recursion call tree
dupNum =int(dupNum/10);
# At this point, if num%10 contains ith
# digit from beginning, then (dupNum)%10
# contains ith digit from end
return (num % 10 == (dupNum) % 10);
# The main function that uses recursive
# function isPalUtil() to find out whether
# num is palindrome or not
def isPal(num):
# If num is negative, make it positive
if (num < 0):
num = -num;
# Create a separate copy of num, so that
# modifications made to address dupNum
# don't change the input number.
dupNum = num; # dupNum = num
return isPalUtil(num, dupNum);
# Function to generate all primes and checking
# whether number is palindromic or not
def printPalPrimesLessThanN(n):
# Create a boolean array "prime[0..n]" and
# initialize all entries it as true. A value
# in prime[i] will finally be false if i is
# Not a prime, else true.
prime = [True] * (n + 1);
p = 2;
while (p * p <= n):
# If prime[p] is not changed,
# then it is a prime
if (prime[p]):
# Update all multiples of p
for i in range(p * 2, n + 1, p):
prime[i] = False;
p += 1;
# Print all palindromic prime numbers
for p in range(2, n + 1):
# checking whether the given number
# is prime palindromic or not
if (prime[p] and isPal(p)):
print(p, end = " ");
# Driver Code
n = 100;
print("Palindromic primes smaller",
"than or equal to", n, "are :");
printPalPrimesLessThanN(n);
# This code is contributed by chandan_jnu
C
// C# Program to print all palindromic
// primes smaller than or equal to n.
using System;
class GFG {
// A function that returns true only
// if num contains one digit
static bool oneDigit(int num)
{
// comparison operation is faster than
// division operation. So using following
// instead of "return num / 10 == 0;"
return (num >= 0 && num < 10);
}
// A recursive function to find out whether
// num is palindrome or not. Initially, dupNum
// contains address of a copy of num.
static bool isPalUtil(int num, int dupNum)
{
// Base case (needed for recursion termination):
// This statement/ mainly compares the first
// digit with the last digit
if (oneDigit(num))
return (num == (dupNum) % 10);
// This is the key line in this method. Note
// that all recursive/ calls have a separate
// copy of num, but they all share same copy
// of dupNum. We divide num while moving up
// the recursion tree
if (!isPalUtil(num/10, dupNum))
return false;
// The following statements are executed when
// we move up the recursion call tree
dupNum /= 10;
// At this point, if num%10 contains ith
// digit from beginning, then (dupNum)%10
// contains ith digit from end
return (num % 10 == (dupNum) % 10);
}
// The main function that uses recursive
// function isPalUtil() to find out
// whether num is palindrome or not
static bool isPal(int num)
{
// If num is negative, make it positive
if (num < 0)
num = -num;
// Create a separate copy of num, so that
// modifications made to address dupNum don't
// change the input number.
int dupNum = num; // dupNum = num
return isPalUtil(num, dupNum);
}
// Function to generate all primes and checking
// whether number is palindromic or not
static void printPalPrimesLessThanN(int n)
{
// Create a boolean array "prime[0..n]" and
// initialize all entries it as true. A value
// in prime[i] will finally be false if i is
// Not a prime, else true.
bool []prime = new bool[n+1];
for (int i=0;i<n+1;i++)
prime[i]=true;
for (int p = 2; p*p <= n; p++)
{
// If prime[p] is not changed,
// then it is a prime
if (prime[p])
{
// Update all multiples of p
for (int i = p*2; i <= n; i += p){
prime[i] = false;}
}
}
// Print all palindromic prime numbers
for (int p = 2; p <= n; p++){
// checking whether the given number is
// prime palindromic or not
if (prime[p] && isPal(p)){
Console.Write(p + " ");
}
}
}
// Driver function
public static void Main()
{
int n = 100;
Console.Write("Palindromic primes smaller than or " +
"equal to are :\n", n);
printPalPrimesLessThanN(n);
}
}
// This code is contributed by nitin mittal.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to print all palindromic
// primes smaller than or equal to n.
// A function that returns true only
// if num contains one digit
function oneDigit($num)
{
// comparison operation is faster than
// division operation. So using following
// instead of "return num / 10 == 0;"
return ($num >= 0 && $num < 10);
}
// A recursive function to find out whether
// num is palindrome or not. Initially,
// dupNum contains address of a copy of num.
function isPalUtil($num, $dupNum)
{
// Base case (needed for recursion termination):
// This statement/ mainly compares the first
// digit with the last digit
if (oneDigit($num))
return ($num == ($dupNum) % 10);
// This is the key line in this method. Note
// that all recursive/ calls have a separate
// copy of num, but they all share same copy
// of dupNum. We divide num while moving up
// the recursion tree
if (!isPalUtil((int)($num/10), $dupNum))
return false;
// The following statements are executed
// when we move up the recursion call tree
$dupNum = (int)($dupNum / 10);
// At this point, if num%10 contains ith
// digit from beginning, then (dupNum)%10
// contains ith digit from end
return ($num % 10 == ($dupNum) % 10);
}
// The main function that uses recursive
// function isPalUtil() to find out whether
// num is palindrome or not
function isPal($num)
{
// If num is negative, make it positive
if ($num < 0)
$num = -$num;
// Create a separate copy of num, so that
// modifications made to address dupNum
// don't change the input number.
$dupNum = $num; // dupNum = num
return isPalUtil($num, $dupNum);
}
// Function to generate all primes and checking
// whether number is palindromic or not
function printPalPrimesLessThanN($n)
{
// Create a boolean array "prime[0..n]" and
// initialize all entries it as true. A value
// in prime[i] will finally be false if i is
// Not a prime, else true.
$prime = array_fill(0, $n + 1, true);
for ($p = 2; $p * $p <= $n; $p++)
{
// If prime[p] is not changed, then
// it is a prime
if ($prime[$p])
{
// Update all multiples of p
for ($i = $p * 2; $i <= $n; $i += $p)
{
$prime[$i] = false;
}
}
}
// Print all palindromic prime numbers
for ($p = 2; $p <= $n; $p++)
{
// checking whether the given number
// is prime palindromic or not
if ($prime[$p] && isPal($p))
{
print($p . " ");
}
}
}
// Driver Code
$n = 100;
print("Palindromic primes smaller " .
"than or equal to ".$n." are :\n");
printPalPrimesLessThanN($n);
// This code is contributed by mits
?>
java 描述语言
<script>
// javascript Program to print all palindromic primes
// smaller than or equal to n.
// A function that returns true only if num
// contains one digit
function oneDigit(num)
{
// comparison operation is faster than
// division operation. So using following
// instead of "return num / 10 == 0;"
return (num >= 0 && num < 10);
}
// A recursive function to find out whether
// num is palindrome or not. Initially, dupNum
// contains address of a copy of num.
function isPalUtil(num , dupNum)
{
// Base case (needed for recursion termination):
// This statement/ mainly compares the first
// digit with the last digit
if (oneDigit(num))
return (num == (dupNum) % 10);
// This is the key line in this method. Note
// that all recursive/ calls have a separate
// copy of num, but they all share same copy
// of dupNum. We divide num while moving up
// the recursion tree
if (!isPalUtil(parseInt(num/10), dupNum))
return false;
// The following statements are executed when
// we move up the recursion call tree
dupNum = parseInt(dupNum/10);
// At this point, if num%10 contains ith
// digit from beginning, then (dupNum)%10
// contains ith digit from end
return (num % 10 == (dupNum) % 10);
}
// The main function that uses recursive function
// isPalUtil() to find out whether num is palindrome
// or not
function isPal(num)
{
// If num is negative, make it positive
if (num < 0)
num = -num;
// Create a separate copy of num, so that
// modifications made to address dupNum don't
// change the input number.
var dupNum = num; // dupNum = num
return isPalUtil(num, dupNum);
}
// Function to generate all primes and checking
// whether number is palindromic or not
function printPalPrimesLessThanN(n)
{
// Create a boolean array "prime[0..n]" and
// initialize all entries it as true. A value
// in prime[i] will finally be false if i is
// Not a prime, else true.
var prime = Array.from({length: n+1}, (_, i) => true);
for (p = 2; p*p <= n; p++)
{
// If prime[p] is not changed, then it is
// a prime
if (prime[p])
{
// Update all multiples of p
for (i = p*2; i <= n; i += p){
prime[i] = false;}
}
}
// Print all palindromic prime numbers
for (p = 2; p <= n; p++){
// checking whether the given number is
// prime palindromic or not
if (prime[p] && isPal(p)){
document.write(p + " ");
}
}
}
// Driver function
var n = 100;
document.write('Palindromic primes smaller than or equal to '+n+' are :<br>');
printPalPrimesLessThanN(n);
// This code is contributed by Princi Singh
</script>
输出:
Palindromic primes smaller than or equal to 100 are :
2 3 5 7 11
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