给定整数N ，任务是检查该数字是否为质数。如果是，则打印该数字及其等于N的幂。否则打印-1。
A prime power is a positive integer power of a single prime number.
For example: 7 = 71, 9 = 32 and 32 = 25 are prime powers, while 6 = 2 × 3, 12 = 22 × 3 and 36 = 62 = 22 × 32 are not. (The number 1 is not counted as a prime power.)
注意：如果没有这样的质数，则打印-1。
例子：
Input: N = 49
Output: 72
Explanation:
N can be represented as a power of prime number 7.
N = 49 = 72
Input: N = 100
Output: -1
Explanation:
N cannot be represented as a power of any prime number.
方法：这个想法是使用Eratosthenes的Seive来找到所有素数。然后，遍历所有素数，并检查是否有任何素数除以给定数N，如果是，则将其除以直到它变成1或被该素数整除。最后，检查该数字是否等于1，如果是，则返回质数，否则给定的数不能表示为质数提高。
下面是上述方法的实现：
C++
// C++ implementation to check if
// a number is a prime power number
#include
using namespace std;
// Array to store the
// prime numbers
bool is_prime[1000001];
vector primes;
// Function to mark the prime
// numbers using Seive of
// Eratosthenes
void SieveOfEratosthenes(int n)
{
int p = 2;
for(int i = 0; i < n; i++)
is_prime[i] = true;
while (p * p <= n)
{
// If prime[p] is not
// changed, then it is a prime
if (is_prime[p] == true)
{
// Update all multiples of p
for(int i = p * p; i < n + 1; i += p)
{
is_prime[i] = false;
}
}
p += 1;
}
for(int i = 2; i < n + 1; i++)
{
if (is_prime[i])
primes.push_back(i);
}
}
// Function to check if the
// number can be represented
// as a power of prime
pair power_of_prime(int n)
{
for(auto i : primes)
{
if (n % i == 0)
{
int c = 0;
while(n % i == 0)
{
n /= i;
c += 1;
}
if(n == 1)
return {i, c};
else
return {-1, 1};
}
}
}
// Driver Code
int main()
{
int n = 49;
SieveOfEratosthenes(int(sqrt(n)) + 1);
// Function Call
pair p = power_of_prime(n);
if (p.first > 1)
cout << p.first << " ^ "
<< p.second << endl;
else
cout << -1 << endl;
}
// This code is contributed by Surendra_Gangwar Java
// Java implementation to check if
// a number is a prime power number
import java.io.*;
import java.util.*;
import java.lang.Math;
class GFG{
// Array to store the
// prime numbers
static ArrayList primes = new ArrayList();
// Function to mark the prime
// numbers using Seive of
// Eratosthenes
public static void sieveOfEratosthenes(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];
for(int i = 0; i < n; 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] == true)
{
// Update all multiples of p
for(int i = p * 2; i <= n; i += p)
prime[i] = false;
}
}
// Print all prime numbers
for(int i = 2; i <= n; i++)
{
if(prime[i] == true)
primes.add(i);
}
}
// Function to check if the
// number can be represented
// as a power of prime
public static int[] power_of_prime(int n)
{
for(int ii = 0; ii < primes.size(); ii++)
{
int i = primes.get(ii);
if (n % i == 0)
{
int c = 0;
while(n % i == 0)
{
n /= i;
c += 1;
}
if(n == 1)
return new int[]{i, c};
else
return new int[]{-1, 1};
}
}
return new int[]{-1, 1};
}
// Driver code
public static void main(String args[])
{
int n = 49;
int sq = (int)(Math.sqrt(n));
sieveOfEratosthenes(sq + 1);
// Function call
int arr[] = power_of_prime(n);
if (arr[0] > 1)
System.out.println(arr[0] + " ^ " + arr[1]);
else
System.out.println("-1");
}
}
// This code is contributed by grand_master Python3
# Python3 implementation to check
# if a number is a prime power number
from math import *
# Array to store the
# prime numbers
is_prime = [True for i in range(10**6 + 1)]
primes =[]
# Function to mark the prime
# numbers using Seive of
# Eratosthenes
def SieveOfEratosthenes(n):
p = 2
while (p * p <= n):
# If prime[p] is not
# changed, then it is a prime
if (is_prime[p] == True):
# Update all multiples of p
for i in range(p * p, n + 1, p):
is_prime[i] = False
p += 1
for i in range(2, n + 1):
if is_prime[i]:
primes.append(i)
# Function to check if the
# number can be represented
# as a power of prime
def power_of_prime(n):
for i in primes:
if n % i == 0:
c = 0
while n % i == 0:
n//= i
c += 1
if n == 1:
return (i, c)
else:
return (-1, 1)
# Driver Code
if __name__ == "__main__":
n = 49
SieveOfEratosthenes(int(sqrt(n))+1)
# Function Call
num, power = power_of_prime(n)
if num > 1:
print(num, "^", power)
else:
print(-1)C#
// C# implementation to check if
// a number is a prime power number
using System;
using System.Collections;
class GFG{
// Array to store the
// prime numbers
static ArrayList primes = new ArrayList();
// Function to mark the prime
// numbers using Seive of
// Eratosthenes
public static void sieveOfEratosthenes(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; 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] == true)
{
// Update all multiples of p
for(int i = p * 2; i <= n; i += p)
prime[i] = false;
}
}
// Print all prime numbers
for(int i = 2; i <= n; i++)
{
if (prime[i] == true)
primes.Add(i);
}
}
// Function to check if the
// number can be represented
// as a power of prime
public static int[] power_of_prime(int n)
{
for(int ii = 0; ii < primes.Count; ii++)
{
int i = (int)primes[ii];
if (n % i == 0)
{
int c = 0;
while (n % i == 0)
{
n /= i;
c += 1;
}
if (n == 1)
return new int[]{i, c};
else
return new int[]{-1, 1};
}
}
return new int[]{-1, 1};
}
// Driver code
public static void Main(string []args)
{
int n = 49;
int sq = (int)(Math.Sqrt(n));
sieveOfEratosthenes(sq + 1);
// Function call
int []arr = power_of_prime(n);
if (arr[0] > 1)
Console.Write(arr[0] + " ^ " +
arr[1]);
else
Console.Write("-1");
}
}
// This code is contributed by rutvik_56输出：
7 ^ 2