8.13动态规划例题：钢条切割

 1 import java.util.Arrays;
 2 
 3 public class Eight_13动态规划例题_钢条切割 {
 4     static int n = 10;
 5     static int[] p = {1,5,8,16,10,17,17,20,24,30};
 6     
 7     //递归
 8     private static int r(int x){
 9         if(x == 0)
10             return 0;
11         
12         int ans = 0;
13         for(int i = 1; i <=x; i++){
14             int v = p[i-1] + r(x-i);
15             ans = Math.max(ans, v);
16         }
17         return ans;
18     }
19     
20     //记忆化递归
21     static int[] vs = new int[n+1];
22     private static int r2(int x){
23         if(x == 0)
24             return 0;
25         
26         int ans = 0;
27         for(int i = 1; i <=x; i++){
28             if(vs[x-i] == -1){
29                 vs[x-i] = r2(x-i);
30             }
31             int v = p[i-1] + vs[x-i];
32             ans = Math.max(ans, v);
33         }
34         vs[x] = ans;
35         return ans;
36     }
37     
38     //dp解法
39     private static int dp(){
40         vs[0] = 0;
41         for(int i = 1; i <= n; i++){ //拥有的钢条长度
42             for(int j = 1; j <= i; j++){ //保留j为整段
43                 vs[i] = Math.max(p[j-1]+vs[i-j], vs[i]);
44             }
45         }
46         return vs[n];
47     }
48     public static void main(String[] args) {
49         System.out.println(r(10));
50         Arrays.fill(vs, -1);
51         System.out.println(r2(10));
52         System.out.println(dp());
53     }
54 }
55