UVa 437 The Tower of Babylon(动态规划)

 The Tower of Babylon 

Perhaps you have heard of the legend of the Tower of Babylon. Nowadays many details of this tale have been forgotten. So now, in line with the educational nature of this contest, we will tell you the whole story:

The babylonians had n types of blocks, and an unlimited supply of blocks of each type. Each type-i block was a rectangular solid with linear dimensions tex2html_wrap_inline32 . 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 wanted to construct the tallest tower possible by stacking blocks. The problem was 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. 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 babylonians can build with a given set of blocks.

Input and Output

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 tex2html_wrap_inline40 , tex2html_wrap_inline42 and tex2html_wrap_inline44 .

Input is terminated by a value of zero (0) for n.

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  给你n种长方体  每种都有无穷个  当一个长方体的长和宽都小于另一个时  这个长方体可以放在另一个上面  要求输出这样累积起来的最大高度

因为每个长方体都有3种放法  比较不好控制   可以把一个长宽高分成三个长方体  高度是固定的  这样就比较好控制了;


#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
#define maxn 105
int x[maxn], y[maxn], z[maxn], d[maxn], n;
int dp(int i)
{
    if(d[i] > 0) return d[i];
    d[i] = z[i];
    for(int j = 1; j <= n; ++j)
    {
        if((x[i] > x[j] && y[i] > y[j]) || (x[i] > y[j] && y[i] > x[j]))
            d[i] = max(d[i], dp(j) + z[i]);
    }
    return d[i];
}

int main()
{
    int a, b, c, cas = 1;
    while (scanf("%d", &n), n)
    {
        n *= 3;
        for(int i = 1; i <= n;)
        {
            scanf("%d%d%d", &a, &b, &c);
            x[i] = a; y[i] = b; z[i++] = c;
            x[i] = a; y[i] = c; z[i++] = b;
            x[i] = b; y[i] = c; z[i++] = a;
        }

        int ans = 0;
        memset(d, 0, sizeof(d));
        for(int i = 1; i <= n; ++i)
            ans = max(dp(i), ans);
        printf("Case %d: maximum height = %d\n", cas, ans);

        cas++;
    }
    return 0;
}


### 关于 Babylon.js 中实现动态避障算法 在 Babylon.js 中,动态避障算法可以通过结合物理引擎、路径规划以及群体导航系统来实现。以下是具体方法和示例: #### 使用 Babylon.js 的 Crowd Navigation System Babylon.js 提供了一个名为 `Crowd Navigation System` 的模块[^1],该模块可以用于模拟人群移动并支持动态避障功能。通过设置目标位置和障碍物参数,可以让对象自动避开其他物体。 ```javascript // 初始化场景 const scene = new BABYLON.Scene(engine); // 创建地面和其他静态几何体作为障碍物 const ground = BABYLON.MeshBuilder.CreateGround("ground", {width: 10, height: 10}, scene); const obstacle = BABYLON.MeshBuilder.CreateBox("obstacle", {size: 2}, scene); obstacle.position.set(3, 0.5, 3); // 设置障碍物的位置 // 添加动态代理 (Dynamic Agent) const crowdSystem = new BABYLON.CrowdNavigationSystem(scene); crowdSystem.addAgent({ position: new BABYLON.Vector3(-4, 0, -4), // 初始位置 targetPosition: new BABYLON.Vector3(4, 0, 4) // 目标位置 }); scene.onBeforeRenderObservable.add(() => { crowdSystem.update(); // 更新群组导航逻辑 }); ``` 此代码片段展示了如何创建一个简单的动态代理,并让其朝向指定的目标前进,同时绕过障碍物。 #### 结合 Web Workers API 加速计算 为了提高性能,特别是当有大量代理需要处理时,可以利用 Web Workers API 将复杂的避障运算卸载到后台线程中运行[^2]。这有助于减少主线程的压力,从而提升用户体验。 ```javascript if (window.Worker) { const worker = new Worker('path/to/worker.js'); worker.postMessage({ agentsPositions: [...], obstacles: [...] }); worker.onmessage = function(e) { console.log('Updated positions:', e.data); }; } else { console.warn('Web Workers not supported.'); } ``` 在此部分中提到的 `worker.js` 文件应包含执行实际碰撞检测与路径调整的相关函数[^2]。 #### 高级动画技术的应用 除了基本的功能外,还可以探索更高级别的动画技巧以增强视觉效果。例如,应用骨骼动画使角色的动作更加自然流畅;或者采用自定义着色器渲染特殊材质等[^3]。 --- ###
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