[POJ][1271][Nice Milk][半平面交]

/*
题目：Nice Milk
题目来源：POJ 1271
题目难度：中等偏难
题目内容或思路：
    半平面交（黑书习题）
    一开始一直TLE，以为是算法可以更优，结果是细节问题。
做题日期：2011.2.28
*/
#include <cstdio>
#include <cstdlib>
#include <climits>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <queue>
#include <map>
#include <vector>
#include <bitset>
#include <cmath>
#include <set>
using namespace std;

const double eps = 1e-8;
const int N = 22;

struct cpoint {
    double x, y;
    cpoint(double x = 0, double y = 0) : x(x), y(y) {}
};

int dcmp(double x){
    if (x < -eps) return -1; else return x > eps;
}

double sqr(double x) {return x * x;}

double dis(cpoint a, cpoint b) {
    return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y));
}

double cross(cpoint p0, cpoint p1, cpoint p2) {
    return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y);
}

struct cvector {
    cpoint s, e;
    double ang, d;
};

void setline(double x1, double y1, double x2, double y2, cvector &v) {
    v.s.x = x1; v.s.y = y1;
    v.e.x = x2; v.e.y = y2;
    v.ang = atan2(y2 - y1, x2 - x1);
    if (dcmp(x1 - x2)) 
        v.d = (x1 * y2 - x2 * y1) / fabs(x1 - x2);
    else 
        v.d = (x1 * y2 - x2 * y1) / fabs(y1 - y2);
}

bool parallel(const cvector &a, const cvector &b) {
    double u = (a.e.x - a.s.x) * (b.e.y - b.s.y)
            - (a.e.y - a.s.y) * (b.e.x - b.s.x);
    return dcmp(u) == 0;
}

cpoint crosspoint(const cvector &a, const cvector &b) {
    cpoint res;
    double u = cross(a.s, a.e, b.s), v = cross(a.e, a.s, b.e);
    res.x = (b.s.x * v + b.e.x * u) / (u + v);
    res.y = (b.s.y * v + b.e.y * u) / (u + v);
    return res;
}

bool veccmp(const cvector &l, const cvector &r) {
    if (dcmp(l.ang - r.ang)) return l.ang < r.ang;
    return l.d < r.d;
}

cvector deq[N];

void HalfPanelCross(cvector vec[], int n, cpoint cp[], int &m) {
    int i, tn; m = 0;
    sort(vec, vec + n, veccmp);
    for (i = tn = 1; i < n; ++i)
        if (dcmp(vec[i].ang - vec[i - 1].ang))
            vec[tn++] = vec[i];
    n = tn;
    int bot = 0, top = 1;
    deq[0] = vec[0];
    deq[1] = vec[1];
    for (i = 2; i < n; ++i) {
        if (parallel(deq[top], deq[top - 1]) ||
            parallel(deq[bot], deq[bot + 1]) )return;
        while (bot < top && dcmp( cross(vec[i].s, vec[i].e,
            crosspoint(deq[top], deq[top - 1])) ) < 0 )
            top--;
        while (bot < top && dcmp( cross(vec[i].s, vec[i].e,
            crosspoint(deq[bot], deq[bot + 1])) ) < 0 )
            bot++;
        deq[++top] = vec[i];
    }
    while (bot < top && dcmp(cross(deq[bot].s, deq[bot].e,
        crosspoint(deq[top], deq[top - 1])) ) < 0 )
        top--;
    while (bot < top && dcmp(cross(deq[top].s, deq[top].e,
        crosspoint(deq[bot], deq[bot + 1])) ) < 0 )
        bot++;
    if (top <= bot + 1) return ;
    for (i = bot; i < top; ++i)
        cp[m++] = crosspoint(deq[i], deq[i + 1]);
    if (bot < top + 1)
        cp[m++] = crosspoint(deq[bot], deq[top]);
    for (i = 0; i < m; ++i) {
        if (dcmp(cp[i].x) == 0) cp[i].x = 0;
        if (dcmp(cp[i].y) == 0) cp[i].y = 0;
    }
}

double PolygonArea(cpoint p[], int n) {
    if (n < 3) return 0;
    double s = p[0].y * (p[n - 1].x - p[1].x);
    for (int i = 1; i < n; ++i)
        s += p[i].y * (p[i - 1].x - p[(i + 1) % n].x);
    return fabs(s / 2);
}

int n, k, h;
cpoint cp[N], tp[N];
cvector v[N], v1[N], v2[N];
int stat[130000], tot;

int cnt(int x) {
    int res = 0;
    while (x) {
        if (x & 1) res++;
        x >>= 1;
    }
    return res;
}

void dfs(int st, int pos, int cnt) {
    if (cnt == k) {
        stat[tot++] = st;
        return;
    }
    if (cnt > k || pos == n || n - pos < k - cnt) return;
    dfs(st, pos + 1, cnt);
    dfs(st + (1 << pos), pos + 1, cnt + 1);
}

void solve() {
    int m;
    for (int i = 0; i < n; ++i) {
        scanf("%lf%lf", &cp[i].x, &cp[i].y);
    }
    k = min(k, n);
    if (k == 0 || h == 0) {
        puts("0.00");
        return ;
    }
    tot = 0;
    dfs(0, 0, 0);
    double res = 1e200;
    for (int i = 0; i < n; ++i) { // 一开始setline都是在下面的循环里面进行的，导致一直TLE
        setline(cp[i].x, cp[i].y, cp[(i + 1) % n].x, cp[(i + 1) % n].y, v1[i]);
        double d = dis(cp[i], cp[(i + 1) % n]);
        double dx = h / d * ( cp[i].y - cp[(i + 1) % n].y);
        double dy = h / d * (-cp[i].x + cp[(i + 1) % n].x);
        setline(cp[i].x + dx, cp[i].y + dy, cp[(i + 1) % n].x + dx,
            cp[(i + 1) % n].y + dy, v2[i]);
    }
    for (int i = 0; i < tot; ++i) {
        int st = stat[i];
        for (int j = 0; j < n; ++j) {
            if (st & (1 << j))
                v[j] = v2[j];// 一开始setline都是在这里进行的，导致一直TLE
            else 
                v[j] = v1[j];// 现在改成了先算好每条边，存在v1[],v2[]中
        }
        HalfPanelCross(v, n, tp, m);
        res = min(res, PolygonArea(tp, m));
    }
    printf("%.2lf\n", PolygonArea(cp, n) - res);
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("D:\\in.txt", "r", stdin);
#endif
    while (scanf("%d%d%d", &n, &k, &h), n + k + h) {
        solve();
    }
    return 0;
}