HDU-1069-Monkey and Banana【DP】

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Monkey and Banana

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 8618    Accepted Submission(s): 4457

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
  

 题解：经典的dp问题，给出n种类型的长方体石块，给出每种的长、宽、高，每种石块有三种摆放方式，数量不限，可以累加着往上放，问最多能放多高？但是有个限定条件，长和宽必须均小于下面石块的长和宽才能放上去。

#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
int n,ans[222];
struct node
{
	int len,wide,high;
}block[222];
bool cmp(node a,node b)
{
	if(a.len==b.len)
		return a.wide<b.wide;
	else
		return a.len<b.len;
}
int main()
{
	int text=0;
	while(scanf("%d",&n)&&n)
	{
		int a,b,c,k=0;
		while(n--)
		{
			scanf("%d %d %d",&a,&b,&c);
			block[k].len=a;block[k].wide=b;block[k++].high=c;
			block[k].len=a;block[k].wide=c;block[k++].high=b;
			block[k].len=b;block[k].wide=c;block[k++].high=a;
			block[k].len=b;block[k].wide=a;block[k++].high=c;
			block[k].len=c;block[k].wide=a;block[k++].high=b;
			block[k].len=c;block[k].wide=b;block[k++].high=a;
		}
		sort(block,block+k,cmp);
		for(int i=0;i<k;i++)
			ans[i]=block[i].high;// 储存从小到大的高度值，如果不先储存下面的比较变换，会引起 block[i].high 变化 
		for(int i=0;i<k;i++)
		{
			for(int j=0;j<i;j++)
			{		// 上面的 sort 排序可能会有相等的元素相邻在一起，所以要加上长度、宽度的判断 
				if(block[i].len>block[j].len&&block[i].wide>block[j].wide&&ans[i]<ans[j]+block[i].high)
				{
					ans[i]=ans[j]+block[i].high;
				}
			}
		}
		sort(ans,ans+k);
		printf("Case %d: maximum height = %d\n",++text,ans[k-1]);
	}
	return 0;
}