bzoj 1007: [HNOI2008]水平可见直线

题目链接：http://www.lydsy.com/JudgeOnline/problem.php?id=1007

解：直线的上表面一定是一个下凹的形状，那么按斜率排序后维护凸包即可。注意将斜率相同的直线特判一下，取B值大的

/*
 * Problem:  
 * Author:  SHJWUDP
 * Created Time:  2015/6/9 星期二 13:36:54
 * File Name: 233.cpp
 * State: 
 * Memo: 
 */
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>

using namespace std;

const double INF=0x7f7f7f7f;
const double eps=1e-7;

const int MaxA=5e4+7;

struct Data {
    double A, B;
    int id;
    bool operator<(const Data& rhs) const {
        if(fabs(A-rhs.A)<eps) return B>rhs.B;
        return A<rhs.A;
    }
} dt[MaxA];

int N;
pair<int, double> stk[MaxA];
int top;
int main() {
#ifndef ONLINE_JUDGE
    freopen("in", "r", stdin);
    //freopen("out", "w", stdout);
#endif
    while(~scanf("%d", &N)) {
        for(int i=0; i<N; i++) {
            scanf("%lf%lf", &dt[i].A, &dt[i].B);
            dt[i].id=i+1;
        }
        sort(dt, dt+N);

        top=0;
        stk[++top]=make_pair(0, -INF);
        for(int i=1; i<N; i++) {
            Data& u=dt[i];
            if(u.A-dt[stk[top].first].A<eps) continue;
            double tmp;
            while(top) {
                pair<int, double>& x=stk[top];
                Data& d=dt[x.first];
                tmp=(u.B-d.B)/(d.A-u.A);
                if(tmp-x.second<eps) top--;
                else break;
            }
            stk[++top]=make_pair(i, tmp);
        }
        vector<int> vec(top);
        for(int i=1; i<=top; i++) {
            vec[i-1]=dt[stk[i].first].id;
        }
        sort(vec.begin(), vec.end());
        for(int i=0; i<top; i++) {
            printf("%d ", vec[i]);
        }
        puts("");
    }
    return 0;
}