Monkey and Banana

Description

A group of researchers are designing an experiment to test the IQ of a monkey. They will hang a banana at the roof of a building, and at the mean time, provide the monkey with some blocks. If the monkey is clever enough, it shall be able to reach the banana by placing one block on the top another to build a tower and climb up to get its favorite food.

The researchers have n types of blocks, and an unlimited supply of blocks of each type. Each type-i block was a rectangular solid with linear dimensions (x_i, y_i, z_i). A block could be reoriented so that any two of its three dimensions determined the dimensions of the base and the other dimension was the height.

They want to make sure that the tallest tower possible by stacking blocks can reach the roof. The problem is that, in building a tower, one block could only be placed on top of another block as long as the two base dimensions of the upper block were both strictly smaller than the corresponding base dimensions of the lower block because there has to be some space for the monkey to step on. This meant, for example, that blocks oriented to have equal-sized bases couldn't be stacked.

Your job is to write a program that determines the height of the tallest tower the monkey can build with a given set of blocks.

Input Specification

The input file will contain one or more test cases. The first line of each test case contains an integer n, representing the number of different blocks in the following data set. The maximum value for n is 30. Each of the next n lines contains three integers representing the values x_i, y_i and z_i. Input is terminated by a value of zero (0) for n.

Output Specification

For each test case, print one line containing the case number (they are numbered sequentially starting from 1) and the height of the tallest possible tower in the format "Case case: maximum height = height"

Sample Input

1
10 20 30
2
6 8 10
5 5 5
7
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
5
31 41 59
26 53 58
97 93 23
84 62 64
33 83 27
0

Sample Output

Case 1: maximum height = 40
Case 2: maximum height = 21
Case 3: maximum height = 28
Case 4: maximum height = 342


//代码如下：

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
structbox
{
    int length;
    int width;
    int h;
};
int max(int a, int b)
{
    if( a > b )
       return a;
    return b;
}
int min(int a,int b)
{
    if( a < b )
       return a;
    return b;
}
box  boxes[31*3];
//用来保存下面一块方块到上面一块方块的高度之和
int temp[31*3];
//将方块按照长以及宽，高从小到大排序！！是从小到大！！！
bool gcd(boxb1, boxb2)
{
    if(b1.length != b2.length)
          return b1.length < b2.length;
     else if(b1.width != b2.width)
          return b1.width < b2.width;
      else
          return b1.h < b2.h;
}
int dp(int n)
{
    sort(boxes,boxes+3*n,gcd);
    temp[0] = boxes[0].h;
    int maxH = temp[0];
 //核心内容，将第i块作为第j块的底，计算出最大的h.并且保存。
     for(int i = 1; i < 3*n;i++)
     {
         temp[i] = 0;
         for(int j = i - 1 ; j >= 0; j--)
           {
               if(boxes[j].length < boxes[i].length &&
                  boxes[j].width < boxes[i].width &&
                  temp[i] < temp[j])
                  {
                      temp[i] = temp[j];
                  }
           }
           temp[i] += boxes[i].h;
           if(maxH < temp[i])
              maxH = temp[i];
     }
    return maxH;
}
int main()
{
    int Icase = 0;
    int n;
    while(cin>>n && n)
    {
        for(int i = 0 ; i < 3*n;i++)
        {
            boxes[i].h = 0;
        }
        memset(temp,0,sizeof(temp));
        Icase++;
        int a,b,c;
        int total = 0;
        for(int i = 0 ; i < n;i++)
        {
            cin>>a>>b>>c;
            boxes[total].length = max(a,b);
            boxes[total].width = min(a,b);
            boxes[total++].h = c;

            boxes[total].length = max(a,c);
            boxes[total].width = min(a,c);
            boxes[total++].h = b;

            boxes[total].length = max(c,b);
            boxes[total].width = min(c,b);
            boxes[total++].h = a;
        }
        cout<<"Case "<<Icase<<": maximum height = "<<dp(n)<<endl;

    }
    return 0;
}