bzoj 2618[Cqoi2006]凸多边形

2618: [Cqoi2006]凸多边形

Time Limit: 5 Sec  Memory Limit: 128 MB

Description

逆时针给出n个凸多边形的顶点坐标，求它们交的面积。例如n=2时，两个凸多边形如下图：

 

则相交部分的面积为5.233。

Input

第一行有一个整数n，表示凸多边形的个数，以下依次描述各个多边形。第i个多边形的第一行包含一个整数m_i，表示多边形的边数，以下m_i行每行两个整数，逆时针给出各个顶点的坐标。

Output

    输出文件仅包含一个实数，表示相交部分的面积，保留三位小数。

Sample Input

2
6
-2 0
-1 -2
1 -2
2 0
1 2
-1 2
4
0 -3
1 -1
2 2
-1 0

Sample Output

5.233

HINT

100%的数据满足：2<=n<=10，3<=m_i<=50，每维坐标为[-1000,1000]内的整数

一道练习半平面交的好题

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#define LL long long 

using namespace std;

const int MAXN = 10000;
const double eps = 1e-6;
int N, m;
int tot = 0;
int head, tail;
int s[MAXN];

inline LL read()
{
    LL x = 0, w = 1; char ch = 0;
    while(ch < '0' || ch > '9') {
        if(ch == '-') {
            w = -1;
        }
        ch = getchar();
    }
    while(ch >= '0' && ch <= '9') {
        x = x * 10 + ch - '0';
        ch = getchar();
    }
    return x * w;
}

struct Point {
    double x, y;
} p[MAXN], n[MAXN];

struct Line {
    Point p, v;
    double k;
} l[MAXN], tmp[MAXN];

Point operator *(Point a, double k)
{
    Point t;
    t = a;
    t.x *= k ,t.y *= k;
    return t;
}

double operator ^(Point a, Point b)
{
    return a.x * b.y - a.y * b.x;        
}

Point operator +(Point a, Point b)
{
    Point t;
    t.x = a.x + b.x, t.y = a.y + b.y;
    return t;    
}

Point operator -(Point a, Point b)
{
    Point t;
    t.x = a.x - b.x, t.y = a.y - b.y;
    return t;        
}

Point inter(Line a, Line b)
{
    Point t, u;
    double S1, S2;
    u = b.p - a.p;
    S1 = u ^ a.v, S2 = a.v ^ b.v;
    t = b.p + b.v * (S1 / S2);
    return t;
}

int sign(double x)
{
    double d = fabs(x);
    if(d <= eps) {
        return 0;
    } else if(x > 0) {
        return 1;
    } else {
        return -1;
    }
}

bool judge(Point p, Line a)
{
    //cout<<p.x<<" "<<p.y<<endl;
    Point u = p - a.p, v = a.v;
//    cout<<u.x<<" "<<u.y<<" "<<v.x<<" "<<v.y<<endl; 
//    cout<<(u ^ v)<<endl;
    if(sign(u ^ v) >= 0) {
        return true;
    }
    return false;
}

bool cmp(Line a, Line b)
{
    if(a.k == b.k) {
        if(judge(a.p, b)) {
            return false;
        } else {
            return true;
        }
    }
    return a.k < b.k;
}

void work()
{
    head = 0, tail = 0;
    for(int i = 1; i <= tot; i++) {
        Point p = inter(l[s[head]], l[s[head + 1]]);
        int x = s[head], y = s[head + 1];
    //    cout<<s[head]<<" "<<s[head + 1]<<" "<<p.x<<" "<<p.y<<endl;
    //    cout<<l[x].p.x<<" "<<l[x].p.y<<" "<<l[x].v.x<<" "<<l[x].v.y<<endl;
    //    cout<<l[y].p.x<<" "<<l[y].p.y<<" "<<l[y].v.x<<" "<<l[y].v.y<<endl;
        //cout<<p.x<<" "<<p.y<<endl;
        while(tail > head + 1 && judge(inter(l[s[tail - 1]], l[s[tail - 2]]), l[i])) {
            tail--;
        }
        while((head + 1 < tail) && judge(inter(l[s[head]], l[s[head + 1]]), l[i])) {    
            head++;
        }
        s[tail++] = i;
    }
    while(tail > head + 1 && judge(inter(l[s[tail - 1]], l[s[tail - 2]]), l[s[head]])) {
        tail--;
    }
    /*while(tail > head + 1 && judge(inter(l[s[head]], l[s[head + 1]]), l[tail - 1])) {
        head++;
    }
    /*for(int i = head; i < tail; i++) {
        cout<<l[s[i]].k<<" ";
    }
    cout<<endl;*/
    double ans = 0;
    int cnt = 0;
    for(int i = head; i < tail - 1; i++) {
        n[++cnt] = inter(l[s[i]], l[s[i + 1]]);
    }
    n[++cnt] = inter(l[s[tail - 1]], l[s[head]]);
    if(cnt == 0 || cnt == 1) {
        printf("0.000
");
        return;
    } 
    for(int i = 1; i <= cnt; i++) {
        ans += n[i] ^ n[i % cnt + 1];
    }
//    cout<<ans<<endl; 
    ans = ans / 2;
    printf("%.3lf
", ans);
}

int main()
{
    N = read();
    for(int i = 1; i <= N; i++) {
        m = read();
        for(int i = 1; i <= m; i++) {
            p[i].x = read(), p[i].y = read();
        }
        for(int i = 1; i <= m; i++) {
            l[++tot].p = p[i];
            l[tot].v = p[i % m + 1] - p[i];
            l[tot].k = atan2(l[tot].v.y, l[tot].v.x);
        //    cout<<l[tot].k<<" "<<" "<<l[tot].p.x<<" "<<l[tot].p.y<<endl;;
        }
        //cout<<endl;
    }
    sort(l + 1, l + tot + 1, cmp);
    int cnt = tot;
    tot = 0;
    for(int i = 1; i <= cnt; i++) {
        if(l[i].k != l[i - 1].k || i == 1) {
            tmp[++tot] = l[i];
        }
    }
    for(int i = 1; i <= tot; i++) {
        l[i] = tmp[i];
    }
    /*for(int i = 1; i <= tot; i++) {
        cout<<l[i].k<<" ";
    }
    cout<<endl;*/
    work();
}