C - Monkey and Banana

文章目录

• 题意如下
• 思路如下
• 题解如下：

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

题意如下

研究人员有n种类型的砖块，每种类型的砖块都有无限个。第i块砖块的长宽高分别用xi，yi，zi来表示。 同时，由于砖块是可以旋转的，每个砖块的3条边可以组成6种不同的长宽高。你的任务是编写一个程序，计算猴子们最高可以堆出的砖块们的高度。

思路如下

我们先结合题目去分析这一题：题目中给了很多种块，而每种砖块的给了三个参数分别是 xi，hi，zi 三个参数中的每个参数都可以作为高，剩下两个参数中，可以任选其中一个作为长，最后剩下的那个参数作为宽，这样每种砖就可以衍生出6种砖，所以虽然每种砖无限个，但是我们却每种砖只能用一个（因为摆放砖块的时候是严格递减的），

这一题我们可以把这题转化成求 最大递减子序列的和，只不过这里的 和与原来所求的和（原来求和是：子序列中的元素的值直接相加，而我们这题的是 子序列的中每个元素(即代表 一个砖块