给定数字N。任务是在给定数字N的除数中找到最大的良好数。如果不存在这样的正整数a> 1,使得a ^ 2是…的除数,则将数字X定义为良好数。 X。
例子:
Input: N = 10
Output: 10
In 1, 2, 5, 10.
10 is the largest good number
Input: N = 12
Output: 6
In 1, 2, 3, 4, 6, 12.
6 is the largest good number
方法:找到N的所有主要除数。假定它们是p1,p2,…,pk(以O(sqrt(n))时间复杂度表示)。如果答案是a,那么我们知道对于每个1 <= I <= k,显然,a不能被pi ^ 2(以及pi的所有更大幂)整除。因此,<= p1×p2×…×pk。而且我们知道p1×p2×…×pk本身就是一个好数字。因此,答案是p1×p2×…×pk。
下面是上述方法的实现:
C++
// CPP program to find the largest, good
// number in the divisors of given number N.
#include
using namespace std;
// function to return distinct prime factors
vector PrimeFactors(int n)
{
// to store distinct prime factors
vector v;
int x = n;
// run a loop upto sqrt(n)
for (int i = 2; i * i <= n; i++) {
if (x % i == 0) {
// place this prime factor in vector
v.push_back(i);
while (x % i == 0)
x /= i;
}
}
// This condition is to handle the case when n
// is a prime number greater than 1
if (x > 1)
v.push_back(x);
return v;
}
// function that returns good number
int GoodNumber(int n)
{
// distinct prime factors
vector v = PrimeFactors(n);
// to store answer
int ans = 1;
// product of all distinct prime
// factors is required answer
for (int i = 0; i < v.size(); i++)
ans *= v[i];
return ans;
}
// Driver code
int main()
{
int n = 12;
// function call
cout << GoodNumber(n);
return 0;
}
Java
// Java program to find the largest, good
// number in the divisors of given number N.
import java.util.*;
class GFG {
// function to return distinct prime factors
static Vector PrimeFactors(int n)
{
// to store distinct prime factors
Vector v = new Vector();
int x = n;
// run a loop upto sqrt(n)
for (int i = 2; i * i <= n; i++) {
if (x % i == 0) {
// place this prime factor in vector
v.add(i);
while (x % i == 0)
x /= i;
}
}
// This condition is to handle the case when n
// is a prime number greater than 1
if (x > 1)
v.add(x);
return v;
}
// function that returns good number
static int GoodNumber(int n)
{
// distinct prime factors
Vector v = new Vector(PrimeFactors(n));
// to store answer
int ans = 1;
// product of all distinct prime
// factors is required answer
for (int i = 0; i < v.size(); i++)
ans *= v.get(i);
return ans;
}
// Driver code
public static void main(String[] args)
{
int n = 12;
// function call
System.out.println(GoodNumber(n));
}
}
// This code is contributed by ihritik
Python 3
# Python 3 program to find the
# largest, good number in the
# divisors of given number N.
# function to return distinct
# prime factors
def PrimeFactors(n):
# to store distinct
# prime factors
v = []
x = n
# run a loop upto sqrt(n)
i = 2
while(i * i <= n):
if (x % i == 0) :
# place this prime factor
# in vector
v.append(i)
while (x % i == 0):
x //= i
i += 1
# This condition is to handle
# the case when n is a prime
# number greater than 1
if (x > 1):
v.append(x)
return v
# function that returns good number
def GoodNumber(n):
# distinct prime factors
v = PrimeFactors(n)
# to store answer
ans = 1
# product of all distinct prime
# factors is required answer
for i in range(len(v)):
ans *= v[i]
return ans
# Driver code
if __name__ == "__main__":
n = 12
# function call
print(GoodNumber(n))
# This code is contributed
# by ChitraNayal
C#
// C# program to find the largest, good
// number in the divisors of given number N.
using System;
using System.Collections.Generic;
public class GFG {
// function to return distinct prime factors
static List PrimeFactors(int n)
{
// to store distinct prime factors
List v = new List();
int x = n;
// run a loop upto sqrt(n)
for (int i = 2; i * i <= n; i++) {
if (x % i == 0) {
// place this prime factor in vector
v.Add(i);
while (x % i == 0)
x /= i;
}
}
// This condition is to handle the case when n
// is a prime number greater than 1
if (x > 1)
v.Add(x);
return v;
}
// function that returns good number
static int GoodNumber(int n)
{
// distinct prime factors
List v = new List(PrimeFactors(n));
// to store answer
int ans = 1;
// product of all distinct prime
// factors is required answer
for (int i = 0; i < v.Count; i++)
ans *= v[i];
return ans;
}
// Driver code
public static void Main(String[] args)
{
int n = 12;
// function call
Console.WriteLine(GoodNumber(n));
}
}
// This code has been contributed by 29AjayKumar
PHP
1)
array_push($v, $x);
return $v;
}
// function that returns good number
function GoodNumber($n)
{
// distinct prime factors
$v = PrimeFactors($n);
// to store answer
$ans = 1;
// product of all distinct prime
// factors is required answer
for ($i = 0; $i < count($v); $i++)
$ans *= $v[$i];
return $ans;
}
// Driver code
$n = 12;
// function call
echo GoodNumber($n);
// This code is contributed by Rajput-Ji
?>
输出:
6