The Fortified Forest（二进制暴力+ 凸包）呜呜呜~~，大佬们都好厉害

最新推荐文章于 2025-06-24 09:32:51 发布

转载最新推荐文章于 2025-06-24 09:32:51 发布 · 715 阅读

本文介绍了一个使用格拉姆扫描算法求解凸包并计算剩余木材量的应用案例。通过详细的C++代码实现，展示了如何从一组树木节点中选择最佳组合以最大化剩余木材量的过程。该算法首先对输入的树木节点进行预处理，然后通过比较不同组合来确定最优解。

https://blog.youkuaiyun.com/Little_boy_z/article/details/78383415#commentBox推荐看这篇博客，里面写的很详细

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
#include<cmath>
#include<vector>
const int esp = 1e-10;
const int maxn = 20;
const int INF = 1<<30;
#define zero(a) (fabs((double)(a)) < esp)
using namespace std;

int n;
struct node{
    int x;
    int y;
    int v;
    int len;
}e[maxn];

vector<node>a;
int judge(node a,node b,node c){
    return (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x);
}

double dis(node a,node b){
    return sqrt(1.00*(b.x-a.x)*(b.x-a.x) + (b.y-a.y)*(b.y-a.y));
}

int cmp(node p1,node p2){
    double x = judge(a[0],p1,p2);
    if(x > 0 || (zero(x) && dis(a[0],p1) < dis(a[0],p2)))  return 1;
    return 0;
}

double Grham(int len){
    if(a.size() == 1)   return len;
    else if(a.size() == 2)  return len-2*dis(a[0],a[1]);
    for(int i = 1 ; i < a.size() ; i++){
        if(a[i].y < a[0]. y || (a[i].y == a[0].y && a[i].x < a[0].x))   swap(a[0],a[i]);
    }
    sort(a.begin()+1,a.end(),cmp);
    vector<node>s;
    s.push_back(a[0]);
    s.push_back(a[1]);
    s.push_back(a[2]);
    for(int i = 3 ; i < a.size() ; i++){
        while(s.size() >= 2 && judge(s[s.size()-2],s[s.size()-1],a[i]) < esp)   s.pop_back();
        s.push_back(a[i]);
    }
    s.push_back(s[0]);
    double ans = 0;
    for(int i = 0 ; i < s.size()-1 ; i++){
        ans += dis(s[i],s[i+1]);
    }
    return len-ans;
}

int main(){
    int cas = 0;
    while(~scanf("%d",&n) && n){
        for(int i = 0 ; i < n ; i++){
            scanf("%d%d%d%d",&e[i].x,&e[i].y,&e[i].v,&e[i].len);
        }
        int best_val = INF,best_num,best_state;
        double best_extra;
        for(int i = 1 ; i < (1<<n)-1 ; i++){
            a.clear();
            int tmp_val = 0,tmp_len = 0;
            for(int j = 0 ; j < n ; j++){
                if(!((1<<j)&i)) a.push_back(e[j]);
                else{
                    tmp_val += e[j].v;
                    tmp_len += e[j].len;
                }
            }
            if(tmp_val > best_val)  continue;
            double extra = Grham(tmp_len);
            //cout<<"aaaaaa:"<<extra<<endl;
            if(extra >= 0){
                if(tmp_val<best_val){
                    best_val = tmp_val;
                    best_num = n-a.size();
                    best_state = i;
                    best_extra = extra;
                }
                else if(tmp_val==best_val && n-a.size() < best_num){
                    best_num = n-a.size();
                    best_state = i;
                    best_extra = extra;
                }
            }
        }
        printf("Forest %d\nCut these trees:",++cas);
        for(int i = 0 ; i < n ;i++){
            if((1<<i)&best_state)   printf(" %d",i+1);
        }
        printf("\nExtra wood: %.2f\n\n",best_extra);

    }
    return 0;
}