HDU 3516 DP 四边形不等式优化 Tree Construction

设d(i, j)为连通第i个点到第j个点的树的最小长度，则有状态转移方程：

d(i, j) = min{ d(i, k) + d(k + 1, j) + p[k].y - p[j].y + p[k+1].x - p[i].x }

然后用四边形不等式优化之。。

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <algorithm>
 5 #include <map>
 6 #define MP make_pair
 7 #define x first
 8 #define y second
 9 using namespace std;
10
11 typedef pair<int, int> PII;
12
13 const int maxn = 1000 + 10;
14 const int INF = 0x3f3f3f3f;
15 int n;
16
17 PII p[maxn];
18
19 int d[maxn][maxn], s[maxn][maxn];
20
21 int main()
22 {
23     while(scanf("%d", &n) == 1 && n)
24     {
25         for(int i = 1; i <= n; i++) scanf("%d%d", &p[i].x, &p[i].y);
26         for(int i = 1; i <= n; i++)
27         {
28             s[i][i + 1] = i;
29             d[i][i + 1] = p[i+1].x - p[i].x + p[i].y - p[i+1].y;
30         }
31
32         for(int l = 3; l <= n; l++)
33         {
34             for(int i = 1; i + l - 1 <= n; i++)
35             {
36                 int j = i + l - 1;
37                 d[i][j] = INF;
38                 for(int k = s[i][j-1]; k <= s[i+1][j]; k++)
39                 {
40                     int t = d[i][k] + d[k+1][j] + p[k].y - p[j].y + p[k+1].x - p[i].x;
41                     if(t < d[i][j])
42                     {
43                         d[i][j] = t;
44                         s[i][j] = k;
45                     }
46                 }
47             }
48         }
49
50         printf("%d\n", d[1][n]);
51     }
52
53     return 0;
54 }

代码君