# 【BZOJ 1137】[POI2009] Wsp 岛屿

### Code

#include<bits/stdc++.h>
#define LL long long
using namespace std;

const int N = 100009;
const double EPS = 1e-6;

int n, m, tot;
vector<int> del[N];
struct Point{
double x, y;
inline Point() {
}
inline Point(double _x, double _y):x(_x), y(_y) {
}
inline Point operator - (const Point &P) const {
return Point(x - P.x, y - P.y);
}
inline Point operator + (const Point &P) {
return Point(x + P.x, y + P.y);
}
inline Point operator * (double d) {
return Point(x * d, y * d);
}
inline double operator * (const Point &P) {
return x * P.y - y * P.x;
}
inline double len() {
return sqrt(x * x + y * y);
}
}p[N];
struct Line{
Point a, b;
double slope;
inline Line() {
}
inline Line(const Point &_a, const Point &_b):a(_a), b(_b) {
}
inline bool operator < (const Line &L) const {
return slope < L.slope;
}
inline Point intersect(const Line &L) {
double s1 = (L.b - L.a) * (b - L.a);
double s2 = (a - L.a) * (L.b - L.a);
return a + (b - a) * (s2 / (s1 + s2));
}
inline bool OnLeft(const Point &P) {
return (b - a) * (P - a) > EPS;
}
}l[N];

char c = getchar(); int ret = 0, f = 1;
for (; c < '0' || c > '9'; f = c == '-'? -1: 1, c = getchar());
for (; '0' <= c && c <= '9'; ret = ret * 10 + c - '0', c = getchar());
return ret * f;
}

inline void HalfPlaneIntersection(Line *arr, int &sz) {
for (int i = 1; i <= sz; i++) {
Point vec = arr[i].b - arr[i].a;
arr[i].slope = atan2(vec.y, vec.x);
}
sort(arr + 1, arr + 1 + sz);
int l = 1, r = 0;
for (int i = 1; i <= sz; i++) {
for (; l < r && !arr[i].OnLeft(arr[r].intersect(arr[r - 1])); r--);
for (; l < r && !arr[i].OnLeft(arr[l].intersect(arr[l + 1])); l++);
arr[++r] = arr[i];
}
for (; l < r - 1 && !arr[l].OnLeft(arr[r].intersect(arr[r - 1])); r--);
sz = 0;
for (int i = l; i <= r; i++) {
arr[++sz] = arr[i];
}
arr[0] = arr[sz];
arr[sz + 1] = arr[1];
}

int main() {
for (int i = 1; i <= n; i++) {
}
for (int i = 1; i <= m; i++) {
del[min(x, y)].push_back(max(x, y));
}
for (int i = 1; i < n; i++) {
sort(del[i].begin(), del[i].end());
int to = n;
while (!del[i].empty() && *--del[i].end() == to) {
to--;
del[i].pop_back();
}
if (i == 1 && to == n) {
printf("%.10lf", (p[1] - p[n]).len());
exit(0);
}
if (to > i) {
l[++tot] = Line(p[to], p[i]);
}
}
l[++tot] = Line(p[1], p[n]);
HalfPlaneIntersection(l, tot);
double ans = -(p[1] - p[n]).len();
Point last = l[1].intersect(l[0]);
for (int i = 1; i <= tot; i++) {
Point cur = l[i].intersect(l[i + 1]);
ans += (cur - last).len();
last = cur;
}
printf("%.10lf\n", ans);
return 0;
}

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