import java.util.*;

public class Main {
    static final int N = 1010;
    static int[][] f = new int[6][N];
    static int[] a = {0, 10, 20, 50, 100};
    static int n;

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);

        n = sc.nextInt();

        f[0][0] = 1;
        for (int i = 1; i <= 4; i++) 
            for (int j = 0; j <= n; j++)
                for (int k = 0; k * a[i] <= j; k++)
                    f[i][j] += f[i - 1][j - k * a[i]];

        System.out.println(f[4][n]);
    }
}

优化k循环

import java.util.*;

public class Main {
    static final int N = 1010;
    static int[][] f = new int[6][N];
    static int[] a = {0, 10, 20, 50, 100};
    static int n;

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);

        n = sc.nextInt();

        f[0][0] = 1;
        for (int i = 1; i <= 4; i++) 
            for (int j = 0; j <= n; j++) {
                f[i][j] = f[i - 1][j];
                if (j >=  a[i]) f[i][j] += f[i][j - a[i]];
            }

        System.out.println(f[4][n]);
    }
}

优化空间到一维数组

使用的都是本层的数据正序遍历即可

import java.util.*;

public class Main {
    static final int N = 1010;
    static int[] f = new int[N];
    static int[] a = {0, 10, 20, 50, 100};
    static int n;

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);

        n = sc.nextInt();

        f[0] = 1;
        for (int i = 1; i <= 4; i++) 
            for (int j = 0; j <= n; j++) {
                if (j >=  a[i]) f[j] += f[j - a[i]];
            }

        System.out.println(f[n]);
    }
}