Monkey and Banana

研究人员设计实验,通过不同尺寸的积木堆叠来测试猴子的智商,目标是达到建筑最高塔。积木可旋转以形成不同高度,但上层积木必须小于下层。使用动态规划算法确定最大高度。

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Monkey and Banana
Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 12486    Accepted Submission(s): 6527


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
解题

刚开始,一点头绪都没有。睡了一觉,看了一部《流浪地球》。早上醒来开始想。

既然是下面的每一层都比上面大,何不把其按面积大小排个序。然后从头开始往后挑。挑的时候注意一下(bs[i].w>bs[j].w&&bs[i].l>bs[j].l)      ||         (bs[i].w>bs[j].l&&bs[i].l>bs[j].w)有两种能。

然后就是dp 最长递增子序列那一套。

#include<iostream>
#include<map>
#include<cstdio>
#include<memory.h>
#include<algorithm>
#include<cstdlib>
using namespace std;
typedef struct bx
{
    int h,w,l,area;
} box;
int cmp(box a,box b)
{
    return a.area<b.area;
}
int main()
{
    int n,k=1;
    box bs[92];
    while(scanf("%d",&n),n!=0)
    {
        int h,w,l;
        for(int i=0; i<3*n;)
        {
            scanf("%d%d%d",&h,&w,&l);//一个正方体有三种可能。
            bs[i].h=h;
            bs[i].l=l;
            bs[i].w=w;
            bs[i++].area=w*l;
            bs[i].h=w;
            bs[i].l=h;
            bs[i].w=l;
            bs[i++].area=h*l;
            bs[i].h=l;
            bs[i].l=w;
            bs[i].w=h;
            bs[i++].area=w*h;
        }
        n*=3;
        sort(bs,bs+n,cmp);

        int maxm[92];
        for(int i=0; i<n; i++)
            maxm[i]=bs[i].h;
//            for(int i=0;i<n;i++)
//            cout<<maxm[i]<<endl;
        for(int i=1; i<n; i++)
        {

            for(int j=0; j<i; j++)
            {
                if((bs[i].w>bs[j].w&&bs[i].l>bs[j].l)||(bs[i].w>bs[j].l&&bs[i].l>bs[j].w))//注意判断的时候横着放不行的话,可以旋转90度。
                    maxm[i]=max(maxm[i],maxm[j]+bs[i].h);//最长递增子序列那一套

            }
        }

        cout<<"Case "<<k++<<": maximum height = "<<*max_element(maxm,maxm+n)<<endl;
    }

}

 

转载于:https://www.cnblogs.com/tttfu/p/10360998.html

### 实现猴子摘香蕉问题的 C 语言程序 为了实现猴子移动到箱子并最终拿到香蕉的过程,完整的解决方案应包括以下几个部分: 1. **定义数据结构** 使用结构体来表示房间内的各个对象及其属性。这有助于清晰地管理不同实体的状态。 2. **初始化状态** 设置初始条件,如猴子、箱子和香蕉的具体位置。 3. **目标检测** 定义何时认为任务已完成的标准,即当猴子站在箱顶且能触及香蕉时。 4. **动作执行** 编写一系列操作函数用于改变当前场景中的物体相对位置关系,比如`move_monkey()` 和 `push_box()` 5. **主循环控制** 创建一个主循环来进行交互式的命令解析与响应机制,直到达成目的为止。 以下是基于上述原则构建的一个简化版C语言源码框架[^1]: ```c #include <stdio.h> #include <stdbool.h> // Define the structure to hold positions of objects. typedef struct { int monkey; int box; int banana; } State; void move_monkey(State *s, int new_pos); bool can_reach_banana(const State* s); int main(void){ // Initialize state with given locations (example values). State initialState = { .monkey=0 , .box=2 , .banana=3 }; printf("Initial setup:\nMonkey at %d\nBox at %d\nBananas at %d.\n", initialState.monkey, initialState.box, initialState.banana ); while (!can_reach_banana(&initialState)){ char action[8]; scanf("%7s",action); // Read user input if(strcmp(action,"go")==0 || strcmp(action,"Go")==0){ int pos; scanf("%d",&pos); move_monkey(&initialState,pos); printf("Moved monkey to position:%d\n",initialState.monkey); } else{ puts("Invalid command."); } // Print updated status after each step printf("\nCurrent Status:\n"); printf("Monkey is now at %d\n", initialState.monkey); printf("The Box remains at %d\n", initialState.box); printf("And Bananas are still hanging from point %d\n", initialState.banana); } puts("Goal achieved! The monkey has reached the bananas!"); } /// Function implementations below... void move_monkey(State *s,int newPos){ (*s).monkey=newPos; } bool can_reach_banana(const State* s){ return ((*s).monkey==(*s).box && (*s).box==(*s).banana)?true:false ; } ``` 此代码实现了基本功能,允许通过简单的命令行界面指导猴子行动直至成功获取香蕉。然而,这段代码仅提供了一个基础版本;实际应用可能还需要考虑更多细节,例如更复杂的环境建模或者错误处理等特性。
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