平滑数字或易碎数字
原文:https://www . geesforgeks . org/p-smooth-numbers-p-fraible-number/
aP-光滑数或P-脆性数是一个最大质因数小于或等于 P 的整数，给定 N 和 P，我们需要编写一个程序来检查它是否 P-脆性。 示例:
Input : N = 24 , P = 7
Output : YES
Explanation : The prime divisors of 24 are 2 and 3 only.
Hence its largest prime factor is 3 which
is less than or equal to 7, it is P-friable.
Input : N = 22 , P = 5
Output : NO
Explanation : The prime divisors are 11 and 2, hence 11>5,
so it is not a P-friable number.
方法是质因数分解数字并存储所有质因数的最大值。如果一个数可以被整除，我们首先把它除以 2，然后从 3 迭代到 Sqrt(n)，得到一个素数除以一个特定数的次数，这个特定数每次减少 n/i，如果它除以 n，就存储质因数 I，我们把我们的数 n 除以它对应的最小质因数，直到 n 变成 1。如果在 n > 2 的末尾，它意味着它是一个质数，所以我们也把它存储为质因数。最后将最大因子与 p 进行比较，检查它是否为 p 光滑数。
C++
// CPP program to check if a number is
// a p-smooth number or not
#include <iostream>
#include<math.h>
using namespace std;
// function to check if number n
// is a P-smooth number or not
bool check(int n, int p)
{
int maximum = -1;
// prime factorise it by 2
while (!(n % 2))
{
// if the number is divisible by 2
maximum = max(maximum, 2);
n = n/2;
}
// check for all the possible numbers
// that can divide it
for (int i = 3; i <= sqrt(n); i += 2)
{
// prime factorize it by i
while (n % i == 0)
{
// stores the maximum if maximum
// and i, if i divides the number
maximum = max(maximum,i);
n = n / i;
}
}
// if n at the end is a prime number,
// then it a divisor itself
if (n > 2)
maximum = max(maximum, n);
return (maximum <= p);
}
// Driver program to test above function
int main()
{
int n = 24, p = 7;
if (check(n, p))
cout << "yes";
else
cout << "no";
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to check if a number is
// a p-smooth number or not
import java.lang.*;
class GFG{
// function to check if number n
// is a P-smooth number or not
static boolean check(int n, int p)
{
int maximum = -1;
// prime factorise it by 2
while ((n % 2) == 0)
{
// if the number is divisible by 2
maximum = Math.max(maximum, 2);
n = n/2;
}
// check for all the possible numbers
// that can divide it
for (int i = 3; i <= Math.sqrt(n); i += 2)
{
// prime factorize it by i
while (n % i == 0)
{
// stores the maximum if maximum
// and i, if i divides the number
maximum = Math.max(maximum,i);
n = n / i;
}
}
// if n at the end is a prime number,
// then it a divisor itself
if (n > 2)
maximum = Math.max(maximum, n);
return (maximum <= p);
}
// Driver program to test
// above function
public static void main(String[] args)
{
int n = 24, p = 7;
if (check(n, p))
System.out.println("yes");
else
System.out.println("no");
}
}
// This code is contributed by
// Smitha Dinesh Semwal
Python 3
# Python 3 program to
# check if a number is
# a p-smooth number or not
import math
# function to check if number n
# is a P-smooth number or not
def check(n, p) :
maximum = -1
# prime factorise it by 2
while (not(n % 2)):
# if the number is divisible by 2
maximum = max(maximum, 2)
n = int(n/2)
# check for all the possible numbers
# that can divide it
for i in range(3,int(math.sqrt(n)), 2):
# prime factorize it by i
while (n % i == 0) :
# stores the maximum if maximum
# and i, if i divides the number
maximum = max(maximum,i)
n = int(n / i)
# if n at the end is a prime number,
# then it a divisor itself
if (n > 2):
maximum = max(maximum, n)
return (maximum <= p)
# Driver program to test above function
n = 24
p = 7
if (check(n, p)):
print( "yes" )
else:
print( "no" )
# This code is contributed by
# Smitha Dinesh Semwal
C
// C# program to check if a number is
// a p-smooth number or not
using System;
class GFG {
// function to check if number n
// is a P-smooth number or not
static bool check(int n, int p)
{
int maximum = -1;
// prime factorise it by 2
while ((n % 2) == 0)
{
// if the number is divisible by 2
maximum = Math.Max(maximum, 2);
n = n / 2;
}
// check for all the possible numbers
// that can divide it
for (int i = 3; i <= Math.Sqrt(n); i += 2)
{
// prime factorize it by i
while (n % i == 0)
{
// stores the maximum if maximum
// and i, if i divides the number
maximum = Math.Max(maximum, i);
n = n / i;
}
}
// if n at the end is a prime number,
// then it a divisor itself
if (n > 2)
maximum = Math.Max(maximum, n);
return (maximum <= p);
}
// Driver program to test
// above function
public static void Main()
{
int n = 24, p = 7;
if (check(n, p))
Console.Write("yes");
else
Console.Write("no");
}
}
// This code is contributed by vt_m.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to check if a number is
// a p-smooth number or not
// function to check if number n
// is a P-smooth number or not
function check($n, $p)
{
$maximum = -1;
// prime factorise it by 2
while (!($n % 2))
{
// if the number is
// divisible by 2
$maximum = max($maximum, 2);
$n = $n / 2;
}
// check for all the possible
// numbers that can divide it
for ($i = 3; $i <= sqrt($n); $i += 2)
{
// prime factorize it by i
while ($n % $i == 0)
{
// stores the maximum if maximum
// and i, if i divides the number
$maximum = max($maximum, $i);
$n = $n / $i;
}
}
// if n at the end is a prime number,
// then it a divisor itself
if ($n > 2)
$maximum = max($maximum, $n);
return ($maximum <= $p);
}
// Driver Code
$n = 24; $p = 7;
if (check($n, $p))
echo("yes");
else
echo("no");
// This code is contributed by Ajit.
?>
java 描述语言
<script>
// Javascript program to check if a number is
// a p-smooth number or not
// function to check if number n
// is a P-smooth number or not
function check(n, p)
{
let maximum = -1;
// prime factorise it by 2
while (!(n % 2))
{
// if the number is divisible by 2
maximum = Math.max(maximum, 2)
n = n/2;
}
// check for all the possible numbers
// that can divide it
var i;
for (i = 3; i*i <= n; i += 2)
{
// prime factorize it by i
while (n % i == 0)
{
// stores the maximum if maximum
// and i, if i divides the number
maximum = Math.max(maximum, i);
n = n / i;
}
}
// if n at the end is a prime number,
// then it a divisor itself
if (n > 2)
maximum = Math.max(maximum, n);
if (maximum <= p)
return true;
else
return false;
}
// Driver Code
let n = 24, p = 7;
if (check(n, p))
document.write("yes");
else
document.write("no");
// This code is contributed by ajaykrsharma132.
</script>
输出:
yes
参考: T3】http://oeis.org/wiki/P-smooth_numbersT5】
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