HDU_1069_Monkey_and_Banana

Monkey and Banana

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 16792    Accepted Submission(s): 8959

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

110 20 3026 8 105 5 571 1 12 2 23 3 34 4 45 5 56 6 67 7 7531 41 5926 53 5897 93 2384 62 6433 83 270

 

Sample Output

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

 

Source

University of Ulm Local Contest 1996 

 

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本题分析：

首先翻译题意。本题就是说，有一个猴子，想要吃香蕉。但是它必须通过垒砖头的形式垒出一个尽可能高的塔才能吃到香蕉。已知砖头的长宽高数据，可以任意定义边是长边还是宽边还是高。问尽可能达到的高度是多少。

本题的关键在于读懂题目，其他的就可以很容易地做出来。据说是一道很经典的DP题目。

代码：

#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>using namespace std;#define maxn 180 + 10struct block{    int x, y, z;};block b[maxn];int dp[maxn];bool cmp(block a, block b){    if(a.x == b.x)        return a.y > b.y;    return a.x > b.x;}int main(){    int xi, yi, zi;    int n;    int kase = 0;    while(scanf("%d", &n) == 1 && n != 0)    {        for(int i = 0; i < n; i++)        {            scanf("%d%d%d", &xi, &yi, &zi);            b[i * 6].x = xi; b[i * 6].y = yi; b[i * 6].z = zi;            b[i * 6 + 1].x = xi; b[i * 6 + 1].y = zi; b[i * 6 + 1].z = yi;            b[i * 6 + 2].x = yi; b[i * 6 + 2].y = xi; b[i * 6 + 2].z = zi;            b[i * 6 + 3].x = yi; b[i * 6 + 3].y = zi; b[i * 6 + 3].z = xi;            b[i * 6 + 4].x = zi; b[i * 6 + 4].y = xi; b[i * 6 + 4].z = yi;            b[i * 6 + 5].x = zi; b[i * 6 + 5].y = yi; b[i * 6 + 5].z = xi;        }        sort(b, b + n * 6, cmp);        for(int i = 0; i < 6 * n; i++)            dp[i] = b[i].z;        int k = 6 * n;        for(int i = k - 2; i >= 0; i--)            for(int j = i + 1; j < k; j++)            {                if(b[i].x > b[j].x && b[i].y > b[j].y)                {                    if(dp[i] < dp[j] + b[i].z)                        dp[i] = dp[j] + b[i].z;                }            }        int ans = dp[0];        for(int i = 0; i < k; i++)        {            if(ans < dp[i])                ans = dp[i];        }        printf("Case %d: maximum height = %d\n", ++kase, ans);    }return 0;}