杭电1069（按长宽从大到小往上堆高塔）

Monkey and Banana（难度：1）

Time Limit: 2000/1000 MS (Java/Others)
Memory Limit: 65536/32768 K (Java/Others)

Problem 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 (xi, yi, zi). 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

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 xi, yi and zi.
Input is terminated by a value of zero (0) for n.

Output

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

思路：

题意：有n种长方体，每种长方体有无限个。用这些长方体堆一个高度最高的塔，要求下面长方体的长和宽大于上面长方体的长宽。

方法：

• 对输入的长宽高进行处理，列举出三种情况；
• 将长方体的长和宽按从大到小的顺序排序；
• 递推公式：dp[i] = max ( dp[i-1] + ta[i].z , dp[i] ) 。

AC代码：

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

struct node{
    int x,y,z,h;
};

bool cmp(node a,node b)
{
    if(a.x==b.x) return a.y>b.y;
    return a.x>b.x;
}

int main()
{
    int n,icase=0;
    node ta[100];
    int dp[100];
    int xx,yy,zz;

    while(cin>>n)
    {
        if(n==0) break;
        int i=0;
        for(int j=0;j<n;j++)
        {//长方体长宽高的三种情况 
            cin>>xx>>yy>>zz;
            ta[i].x=min(xx,yy);
            ta[i].y=max(xx,yy);
            ta[i].z=zz;
            ta[i+1].x=min(xx,zz);
            ta[i+1].y=max(xx,zz);
            ta[i+1].z=yy;
            ta[i+2].x=min(yy,zz);
            ta[i+2].y=max(yy,zz);
            ta[i+2].z=xx;
            i+=3;
        }
        n=i;
        sort(ta,ta+n,cmp); 
        int hmax=0;
        for(int i=0;i<n;i++)
        {
            dp[i]=ta[i].z;//初始的高(从大到小排序,i越小长方体越大) 
            for(int j=i-1;j>=0;j--)//j是i下面一个
            {
                if(ta[j].x>ta[i].x&&ta[j].y>ta[i].y)//下面比上面大 
                {
                    if(dp[i]<dp[j]+ta[i].z)
                    {
                        dp[i]=dp[j]+ta[i].z;//递推 
                    }
                }
            }
            if(dp[i]>hmax) hmax=dp[i];
        }
        cout<<"Case "<<++icase<<": maximum height = "<<hmax<<endl;
    }
    return 0;
}