poj2767

题意：一些圆台形(中空，厚度忽略不计)的碗，罗在一起，问最小高度是多少。

分析：枚举所有情况，每放一个碗，就要记录其碗底的高度。记录碗底高度的方法是，枚举下面所有的碗，把想象中把这个碗与下面的碗直接叠放在一起，看碗底的高度，取最大值，得到这个碗底的真实高度。每次罗起了所有的碗，就根据每个碗碗底的高度计算其碗顶的高度，并取最大值，即为本次罗碗的高度。不断更新最终结果，取最小值。

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
usingnamespace std;

#define maxn 10

struct Bowl
{
    int r1, r2, h;
} bowl[maxn];

bool vis[maxn];
int sel[maxn];
int ans, n;
double height[maxn];

void input()
{
    scanf("%d", &n);
    for (int i =0; i < n; i++)
        scanf("%d%d%d", &bowl[i].h, &bowl[i].r1, &bowl[i].r2);
}

double inc(int a, int b)
{
    if (bowl[b].r1 >= bowl[a].r2)
        return bowl[a].h;
    if (bowl[b].r2 <= bowl[a].r1)
        return0;
    double ret =0;
    if (bowl[b].r1 >= bowl[a].r1)
        ret = max(ret, bowl[a].h * (bowl[b].r1 - bowl[a].r1) *1.0/ (bowl[a].r2
                - bowl[a].r1));
    if (bowl[b].r2 <= bowl[a].r2)
        ret = max(ret, bowl[a].h * (bowl[b].r2 - bowl[a].r1) *1.0/ (bowl[a].r2
                - bowl[a].r1) - bowl[b].h);
    if (bowl[b].r2 > bowl[a].r2)
        ret = max(ret, bowl[a].h - bowl[b].h * (bowl[a].r2 - bowl[b].r1) *1.0
                / (bowl[b].r2 - bowl[b].r1));
    return ret;
}

void find(int x, int a)
{
    height[x] =0;
    for (int i =0; i < x; i++)
        height[x] = max(height[x], height[i] + inc(sel[i], a));
}

void dfs(int step)
{
    if (step == n)
    {
        int temp =0;
        for (int i =0; i < n; i++)
            temp = max(temp, (int) (height[i] + bowl[sel[i]].h));
        ans = min(ans, temp);
        return;
    }
    for (int i =0; i < n; i++)
        if (!vis[i])
        {
            vis[i] =true;
            sel[step] = i;
            find(step, i);
            dfs(step +1);
            vis[i] =false;
        }
}

int main()
{
    //freopen("t.txt", "r", stdin);
int t;
    scanf("%d", &t);
    while (t--)
    {
        input();
        memset(vis, 0, sizeof(vis));
        ans =0x3f3f3f3f;
        dfs(0);
        printf("%d\n", ans);
    }
    return0;
}