hdu 1069 最长上升子序列变形

因为每种block都有无限多个，所以(x,y,z)等价于是(x,y,z)+(x,z,y)+(y,z,x)这三种block。

然后就像是矩形嵌套那样求解，只不过状态转移方程变成了：

　　dp[i] = max( dp[i], dp[j] + z[i] );

代码如下：

 1 #include <algorithm>
 2 #include <cstdio>
 3 using namespace std;
 4
 5 const int N = 100;
 6 int dp[N];
 7
 8 struct Node
 9 {
10     int x, y, z;
11     bool operator < ( const Node & o ) const
12     {
13         if ( x != o.x ) return x < o.x;
14         return y < o.y;
15     }
16     Node(){}
17     Node( int _x, int _y, int _z )
18     {
19         x = _x, y = _y, z = _z;
20     }
21     void standard()
22     {
23         if ( x > y ) swap( x, y );
24     }
25 } node[N];
26
27 int main ()
28 {
29     int n, _case = 1;
30     while ( scanf("%d", &n), n )
31     {
32         for ( int i = 0; i < n; i++ )
33         {
34             int x, y, z;
35             scanf("%d%d%d", &x, &y, &z);
36             node[i * 3] = Node( x, y, z );
37             node[i * 3].standard();
38             node[i * 3 + 1] = Node( x, z, y );
39             node[i * 3 + 1].standard();
40             node[i * 3 + 2] = Node( y, z, x );
41             node[i * 3 + 2].standard();
42         }
43         sort( node, node + 3 * n );
44         int ans = -1;
45         for ( int i = 0; i < 3 * n; i++ )
46         {
47             dp[i] = node[i].z;
48             for ( int j = 0; j < i; j++ )
49             {
50                 if ( node[j].x < node[i].x && node[j].y < node[i].y )
51                 {
52                     dp[i] = max( dp[i], dp[j] + node[i].z );
53                 }
54             }
55             ans = max( ans, dp[i] );
56         }
57         printf("Case %d: maximum height = %d\n", _case++, ans);
58     }
59     return 0;
60 }