题解 | 整数分解

import java.util.Arrays;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        boolean[] isPrime = new boolean[n + 1];
        List<Integer> primes = new LinkedList<>();
        Arrays.fill(isPrime, true);
        isPrime[0] = isPrime[1] = false;
        for (int i = 2; i <= n; i++) {
            if (isPrime[i]) primes.add(i);
            for (int x : primes) {
                if (i * x > n) break;
                isPrime[i * x] = false;
                if (i % x == 0) break;
            }
        }
        long[] dp = new long[n + 1];
        dp[0] = 1;
        for (int x : primes) for (int i = x; i <= n; i++) dp[i] += dp[i - x];
        System.out.println(dp[n]);
    }
}