原文:
给定一个整数 n ，任务是打印所有的 ≤ n 。 半素数是可以表示为两个不同素数乘积的整数。 比如 15 = 3 * 5 是半素数但是 9 = 3 * 3 不是。
示例:
输入:n = 20 t3】输出: 6 10 14 15
输入:n = 50 t3】输出: 6 10 14 15 21 22 26 33 34 35 38 39 46
先决条件:
方法:对于每一个数字 < n ，计算它所具有的质因数的数量。如果素数的个数是 2 ，那么这个数就是一个半素数，因为所有的半素数只有 2 个素数。
下面是上述方法的实现:
c
// c implementation of the approach
#include
using namespace std;
// function to create sieve for semi prime numbers
vector createsemiprimesieve(int n)
{
int v[n 1];
// this array will initially store the indexes
// after performing below operations if any
// element of array becomes 1 this means
// that the given index is a semi-prime number
// storing indices in each element of vector
for (int i = 1; i <= n; i )
v[i] = i;
int countdivision[n 1];
for (int i = 0; i < n 1; i )
countdivision[i] = 2;
// this array will initially be initialized by 2 and
// will just count the divisions of a number
// as a semiprime number has only 2 prime factors
// which means after dividing by the 2 prime numbers
// if the index countdivision[x] = 0 and v[x] = 1
// this means that x is a semiprime number
// if number a is prime then its
// countdivision[a] = 2 and v[a] = a
for (int i = 2; i <= n; i ) {
// if v[i] != i this means that it is
// not a prime number as it contains
// a divisor which has already divided it
// same reason if countdivision[i] != 2
if (v[i] == i && countdivision[i] == 2) {
// j goes for each factor of i
for (int j = 2 * i; j <= n; j = i) {
if (countdivision[j] > 0) {
// dividing the number by i
// and storing the dividend
v[j] = v[j] / i;
// decreasing the countdivision
countdivision[j]--;
}
}
}
}
// a new vector to store all semi primes
vector res;
for (int i = 2; i <= n; i ) {
// if a number becomes one and
// its countdivision becomes 0
// it means the number has
// two prime divisors
if (v[i] == 1 && countdivision[i] == 0)
res.push_back(i);
}
return res;
}
// driver code
int main()
{
int n = 16;
vector semiprime = createsemiprimesieve(n);
// print all semi-primes
for (int i = 0; i < semiprime.size(); i )
cout << semiprime[i] << " ";
return 0;
}
java 语言(一种计算机语言，尤用于创建网站)
import java.util.*;
// java implementation of the approach
class gfg
{
// function to create sieve for semi prime numbers
static vector createsemiprimesieve(int n)
{
int v[] = new int[n 1];
// this array will initially store the indexes
// after performing below operations if any
// element of array becomes 1 this means
// that the given index is a semi-prime number
// storing indices in each element of vector
for (int i = 1; i <= n; i )
{
v[i] = i;
}
int countdivision[] = new int[n 1];
for (int i = 0; i < n 1; i )
{
countdivision[i] = 2;
}
// this array will initially be initialized by 2 and
// will just count the divisions of a number
// as a semiprime number has only 2 prime factors
// which means after dividing by the 2 prime numbers
// if the index countdivision[x] = 0 and v[x] = 1
// this means that x is a semiprime number
// if number a is prime then its
// countdivision[a] = 2 and v[a] = a
for (int i = 2; i <= n; i )
{
// if v[i] != i this means that it is
// not a prime number as it contains
// a divisor which has already divided it
// same reason if countdivision[i] != 2
if (v[i] == i && countdivision[i] == 2)
{
// j goes for each factor of i
for (int j = 2 * i; j <= n; j = i)
{
if (countdivision[j] > 0)
{
// dividing the number by i
// and storing the dividend
v[j] = v[j] / i;
// decreasing the countdivision
countdivision[j]--;
}
}
}
}
// a new vector to store all semi primes
vector res = new vector<>();
for (int i = 2; i <= n; i )
{
// if a number becomes one and
// its countdivision becomes 0
// it means the number has
// two prime divisors
if (v[i] == 1 && countdivision[i] == 0) {
res.add(i);
}
}
return res;
}
// driver code
public static void main(string[] args)
{
int n = 16;
vector semiprime = createsemiprimesieve(n);
// print all semi-primes
for (int i = 0; i < semiprime.size(); i )
{
system.out.print(semiprime.get(i) " ");
}
}
}
/* this code contributed by princiraj1992 */
python 3
# python 3 implementation of the approach
# function to create sieve for semi prime numbers
def createsemiprimesieve(n):
v = [0 for i in range(n 1)]
# this array will initially store the indexes
# after performing below operations if any
# element of array becomes 1 this means
# that the given index is a semi-prime number
# storing indices in each element of vector
for i in range(1, n 1):
v[i] = i
countdivision = [0 for i in range(n 1)]
for i in range(n 1):
countdivision[i] = 2
# this array will initially be initialized by 2 and
# will just count the divisions of a number
# as a semiprime number has only 2 prime factors
# which means after dividing by the 2 prime numbers
# if the index countdivision[x] = 0 and v[x] = 1
# this means that x is a semiprime number
# if number a is prime then its
# countdivision[a] = 2 and v[a] = a
for i in range(2, n 1, 1):
# if v[i] != i this means that it is
# not a prime number as it contains
# a divisor which has already divided it
# same reason if countdivision[i] != 2
if (v[i] == i and countdivision[i] == 2):
# j goes for each factor of i
for j in range(2 * i, n 1, i):
if (countdivision[j] > 0):
# dividing the number by i
# and storing the dividend
v[j] = int(v[j] / i)
# decreasing the countdivision
countdivision[j] -= 1
# a new vector to store all semi primes
res = []
for i in range(2, n 1, 1):
# if a number becomes one and
# its countdivision becomes 0
# it means the number has
# two prime divisors
if (v[i] == 1 and countdivision[i] == 0):
res.append(i)
return res
# driver code
if __name__ == '__main__':
n = 16
semiprime = createsemiprimesieve(n)
# print all semi-primes
for i in range(len(semiprime)):
print(semiprime[i], end = " ")
# this code is contributed by
# surendra_gangwar
c
// c# implementation of the approach
using system;
using system.collections;
class gfg
{
// function to create sieve for semi prime numbers
static arraylist createsemiprimesieve(int n)
{
int[] v = new int[n 1];
// this array will initially store the indexes
// after performing below operations if any
// element of array becomes 1 this means
// that the given index is a semi-prime number
// storing indices in each element of vector
for (int i = 1; i <= n; i )
v[i] = i;
int[] countdivision = new int[n 1];
for (int i = 0; i < n 1; i )
countdivision[i] = 2;
// this array will initially be initialized by 2 and
// will just count the divisions of a number
// as a semiprime number has only 2 prime factors
// which means after dividing by the 2 prime numbers
// if the index countdivision[x] = 0 and v[x] = 1
// this means that x is a semiprime number
// if number a is prime then its
// countdivision[a] = 2 and v[a] = a
for (int i = 2; i <= n; i )
{
// if v[i] != i this means that it is
// not a prime number as it contains
// a divisor which has already divided it
// same reason if countdivision[i] != 2
if (v[i] == i && countdivision[i] == 2)
{
// j goes for each factor of i
for (int j = 2 * i; j <= n; j = i)
{
if (countdivision[j] > 0)
{
// dividing the number by i
// and storing the dividend
v[j] = v[j] / i;
// decreasing the countdivision
countdivision[j]--;
}
}
}
}
// a new vector to store all semi primes
arraylist res = new arraylist();
for (int i = 2; i <= n; i )
{
// if a number becomes one and
// its countdivision becomes 0
// it means the number has
// two prime divisors
if (v[i] == 1 && countdivision[i] == 0)
res.add(i);
}
return res;
}
// driver code
static void main()
{
int n = 16;
arraylist semiprime = createsemiprimesieve(n);
// print all semi-primes
for (int i = 0; i < semiprime.count; i )
console.write((int)semiprime[i] " ");
}
}
// this code is contributed by mits
服务器端编程语言（professional hypertext preprocessor 的缩写）
0)
{
// dividing the number by i
// and storing the dividend
$v[$j] = $v[$j] / $i;
// decreasing the countdivision
$countdivision[$j]--;
}
}
}
}
// a new vector to store all semi primes
$res = array();
for ($i = 2; $i <= $n; $i )
{
// if a number becomes one and
// its countdivision becomes 0
// it means the number has
// two prime divisors
if ($v[$i] == 1 && $countdivision[$i] == 0)
array_push($res, $i);
}
return $res;
}
// driver code
$n = 16;
$semiprime= array();
$semiprime = createsemiprimesieve($n);
// print all semi-primes
for ($i = 0; $i < count($semiprime); $i )
echo $semiprime[$i], " ";
// this code is contributed by ihritik
?>
java 描述语言
output:
6 10 14 15
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