质数分解2019

把2019分成若干个素数相加，求有多少种分法?
元素完全相同的算同一种方法，比如2+2017=2019和2017+2=2019

package DP;

public class 质数分解2019 {
    static long res = 0;
    static int primes[] = new int[2019];
    static long f[][] = new long[350][2100];
    public static void main(String[] args) {
        for (int i = 0; i < 350; i++) {
            for (int j = 0; j < 2100; j++) {
                f[i][j] = -1;
            }
        }
        int cnt = 0;
        for (int i = 2; i <= 2019; i++) {//初始化1~2019的所有素数
            if (isPrimes(i)) {
                primes[++cnt] = i;
            }
        }
        
        //记忆化搜索
        System.out.println(dfs(1, 2019));
        //一维DP
        dp_1D();
        //二维DP
        dp_2D();
        
    }
    private static void dp_2D() {
        long  a[][]= new long[307][2020];
        for(int i = 0; i <= 306; i ++) a[i][0] = 1;
        for(int i=1;i<=306;i++) {
           for(int j = 0; j <= 2019; j ++) {
               a[i][j] = a[i-1][j];
               if(j-primes[i]>=0) 
                   a[i][j] += a[i-1][j-primes[i]];
           }
        }
        long max = 0;
        for(int i = 1; i <=306; i++) {
            max = Math.max(max, a[i][2019]);
        }
        System.out.println(max);
    }
    private static void dp_1D() {
        long  a[]= new long[2020];
        a[0] = 1;
        for(int i=1;i<=306;i++) {
           for(int j = 2019  ; j >=0; j --) {
               if(j-primes[i]>=0) a[j] += a[j-primes[i]];
           }
        }
        System.out.println(a[2019]);
    }
    private static long dfs(int i, int j) {
        if (j == 0) return 1;
        if (i > 306 || j < primes[i])return 0;
        if (f[i][j] != -1)return f[i][j];
        
        f[i + 1][j-primes[i]]  = dfs(i + 1, j - primes[i]);
        
        f[i + 1][j] = dfs(i + 1, j); 
        
        return f[i][j] = f[i + 1][j-primes[i]] + f[i + 1][j];
    }

    private static boolean isPrimes(int x) {
        for (int i = 2; i <= x / i; i++) {
            if (x % i == 0)
                return false;
        }
        return true;
    }
}