[演算法]: 素數篩法

O(NlogN)篩法

C++

#include <iostream>
using namespace std;

#define maxn 1000000

bool valid[maxn];

void getPrime(int n, int& tot, int ans[maxn]) {
    tot = 0;
    int i, j;
    for (i = 2; i <= n; i++) valid[i] = true;
    for (i = 2; i <= n; i++) if (valid[i]) {
        ans[++tot] = i;
        for (j = i * i; j <= n; j += i) valid[j] = false;
    }
}

int main() {
    int n = 100;
    int tot = 0;
    int ans[maxn];
    getPrime(n, tot, ans);
    for (int i = 1; i <= tot; i++) {
        cout << ans[i] << " ";
    }
    cout << endl << "total: " << tot << endl;
    return 0;
}

JAVA

public class Prime {
    private static boolean[] valid;
    public static int getPrime(int n, int[] ans) {
        int tot = 0;
        valid = new boolean[n + 1];
        int i, j;
        for (i = 2; i <= n; i++) valid[i] = true;
        for (i = 2; i <= n; i++) if (valid[i]) {
            ans[++tot] = i;
            for (j = i * i; j <= n; j += i) valid[j] = false;
        }
        return tot;
    }

    public static void main(String[] args) {
        int n = 100;
        int[] ans = new int[n + 1];
        int tot = getPrime(n, ans);
        for (int i = 1; i <= tot; i++) {
            System.out.print(ans[i]);
            if (i < tot) System.out.print(", ");
            else System.out.println();
        }
        System.out.println("total: " + tot);
    }
}

Python

def getPrime(n, tot_, ans):
    tot = 0
    valid = [True for i in range(n + 1)]
    for i in range(2, n):
        if valid[i]:
            tot += 1
            ans[tot] = i
            for j in range(i * i, n + 1, i):
                valid[j] = False
    tot_[0] = tot


if __name__ == '__main__':
    n = 100
    tot = [0]
    ans = [0 for i in range(n + 1)]
    getPrime(n, tot, ans)
    for i in range(1, tot[0] + 1):
        print(ans[i], end=',')
    print()
    print(tot[0])

O(N)篩法

C++

#include <iostream>
using namespace std;

#define maxn 1000000

bool valid[maxn];

void getPrime(int n, int& tot, int ans[maxn]) {
    tot = 0;
    memset(valid, true, sizeof(valid));
    for (int i = 2; i <= n; i++) {
        if (valid[i]) {
            ++tot;
            ans[tot] = i;
        }
        for (int j = 1; ((j <= tot) && (i * ans[j] <= n)); j++) {
            valid[i * ans[j]] = false;
            if (i % ans[j] == 0) break;
        }
    }
}

int main() {
    int n = 100;
    int tot = 0;
    int ans[maxn];
    getPrime(n, tot, ans);
    for (int i = 1; i <= tot; i++) {
        cout << ans[i] << " ";
    }
    cout << endl << "total: " << tot << endl;
    return 0;
}

JAVA

import java.util.Arrays;

public class Prime {
    private static boolean[] valid;
    public static int getPrime(int n, int[] ans) {
        int tot = 0;
        valid = new boolean[n + 1];
        Arrays.fill(valid, true);
        for (int i = 2; i <= n; i++) {
            if (valid[i]) {
                ans[++tot] = i;
            }
            for (int j = 1; ((j <= tot) && (i * ans[j]) <= n); j++) {
                valid[i * ans[j]] = false;
                if (i % ans[j] == 0) break;
            }
        }
        return tot;
    }

    public static void main(String[] args) {
        int n = 100;
        int[] ans = new int[n + 1];
        int tot = getPrime(n, ans);
        for (int i = 1; i <= tot; i++) {
            System.out.print(ans[i]);
            if (i < tot) System.out.print(", ");
            else System.out.println();
        }
        System.out.println("total: " + tot);
    }
}

Python

def getPrime(n, tot_, ans):
    tot = 0
    valid = [True for i in range(n + 1)]
    for i in range(2, n):
        if valid[i]:
            tot += 1
            ans[tot] = i
        for j in range(1, tot + 1):
            if i * ans[j] > n:
                break
            valid[i * ans[j]] = False
            if i % ans[j] == 0:
                break
    tot_[0] = tot


if __name__ == '__main__':
    n = 100
    tot = [0]
    ans = [0 for i in range(n + 1)]
    getPrime(n, tot, ans)
    for i in range(1, tot[0] + 1):
        print(ans[i], end=',')
    print()
    print(tot[0])