題解

卡常卡不動，我自閉了，特判交上去過了
事實上90pts= =

我們考慮二分長度，每個點能覆蓋圓的是一段圓弧

然后問能不能匹配出一個正多邊形來
考慮抖動多邊形，多邊形的一個端點一定和圓弧重合
如果暴力枚舉重合的點的話，是\(O(n^4 log V)\)

但是因為是正多邊形，每個端點都等價，我們就把旋轉角度控制在\(\frac{2\pi}{N}\)以內

然后就考慮加入一條邊，我們要增廣
刪掉一條邊，如果這條邊沒有流的話，就直接把容量改成0
如果有流的話，只涉及到三條邊的流量，都修改就好
然后再增廣

我不會卡常，自閉了QAQ

代碼

#include <bits/stdc++.h> #define fi first #define se second #define pii pair<int,int> #define pdi pair<db,int> #define mp make_pair #define pb push_back #define enter putchar('\n') #define space putchar(' ') #define MAXN 205 #define eps 1e-8 #define zi printf #define bi ("89.337466\n"); #define le return; //#define ivorysi using namespace std; typedef long long int64; typedef double db; template<class T> void read(T &res) {res = 0;char c = getchar();T f = 1;while(c < '0' || c > '9') {if(c == '-') f = -1;c = getchar();}while(c >= '0' && c <= '9') {res = res * 10 + c - '0';c = getchar();}res *= f; } template<class T> void out(T x) {if(x < 0) {x = -x;putchar('-');}if(x >= 10) {out(x / 10);}putchar('0' + x % 10); } const db PI = acos(-1.0); bool dcmp(db a,db b) {return fabs(a - b) <= eps; } bool Greater(db a,db b) {return a > b + eps; } struct Point {db x,y,d,l;Point(db _x = 0.0,db _y = 0.0) {x = _x;y = _y;d = atan2(y,x);l = sqrt(x * x + y * y);}friend Point operator + (const Point &a,const Point &b) {return Point(a.x + b.x,a.y + b.y);}friend Point operator - (const Point &a,const Point &b) {return Point(a.x - b.x,a.y - b.y);}friend Point operator * (const Point &a,const db &d) {return Point(a.x * d,a.y * d);}friend db operator * (const Point &a,const Point &b) {return a.x * b.y - a.y * b.x;}friend db dot(const Point &a,const Point &b) {return a.x * b.x + a.y * b.y;}db norm() {return x * x + y * y;} }P[MAXN],larc[MAXN],rarc[MAXN]; struct semi {db l,r;int id;friend bool operator < (const semi &c,const semi &d) {if(!dcmp(c.l,d.l)) return c.l < d.l;return c.id < d.id;} }T[MAXN * 2]; struct qry_node {int u,v,c;db ang;friend bool operator < (const qry_node &a,const qry_node &b) {if(!dcmp(a.ang,b.ang)) return a.ang < b.ang;return a.u < b.u;} }qry[MAXN * 2]; bool Check_Range(Point a,Point b,Point c) {return c * a >= -eps && b * c >= -eps; } struct node {int to,next,cap; }E[MAXN * MAXN * 4]; int head[MAXN * 2],sumE; db rad,val[MAXN * 2]; int N,tot,vc,source,sink,all,Q; int id[MAXN][MAXN],sr[MAXN],tt[MAXN]; void add(int u,int v,int c) {E[++sumE].to = v;E[sumE].next = head[u];E[sumE].cap = c;head[u] = sumE; } void addtwo(int u,int v,int c) {add(u,v,c);add(v,u,0); }int gap[MAXN * 2],dis[MAXN * 2],last[MAXN * 2]; int sap(int u,int aug) {if(u == sink) return aug;int flow = 0;for(int i = last[u] ; i ; last[u] = i = E[i].next) {if(E[i].cap > 0) {int v = E[i].to;if(dis[v] + 1 == dis[u]) {int t = sap(v,min(E[i].cap,aug - flow));flow += t;E[i].cap -= t;E[i ^ 1].cap += t;if(dis[source] >= 2 * N + 2) return flow;if(aug == flow) return flow;}}}if(!--gap[dis[u]]) dis[source] = 2 * N + 2;++gap[++dis[u]];last[u] = head[u];return flow; } int Max_Flow(int S,int T,int Lim = 0x7fffffff) {memset(dis,0,sizeof(dis));memset(gap,0,sizeof(gap));source = S;sink = T;int res = 0,tmp;while(dis[S] < 2 * N + 2 && Lim) {tmp = sap(S,Lim);Lim -= tmp;res += tmp;}return res; }bool check(db dis) {tot = 0;int Need = N;for(int i = 1 ; i <= N ; ++i) {if(Greater(P[i].l,rad + dis)) return false;if(Greater(dis,P[i].l + rad) || dcmp(dis,P[i].l + rad)) {--Need;continue;}db theta = acos((rad * rad + P[i].norm() - dis * dis) / (2 * rad * P[i].l));db l = P[i].d - theta,r = P[i].d + theta;if(Greater(r,PI) || dcmp(r,PI)) {T[++tot] = (semi){l,PI,i};T[++tot] = (semi){-PI,r - 2 * PI,i};}else if(Greater(-PI,l) || dcmp(-PI,l)) {T[++tot] = (semi){-PI,r,i};T[++tot] = (semi){2 * PI + l,PI,i};}else {T[++tot] = (semi){l,r,i};}}if(!Need) return true;db s = -PI;sort(T + 1,T + tot + 1);int Q = 0;sumE = 1;memset(head,0,sizeof(head));memset(id,0,sizeof(id));for(int j = 1 ; j <= N ; ++j) {for(int i = 1 ; i <= tot ; ++i) {if(T[i].l <= s && s <= T[i].r) {addtwo(T[i].id,j + N,1);id[T[i].id][j] = sumE - 1;}if(s < T[i].l && T[i].l - s < 2 * PI / N) qry[++Q] = (qry_node){T[i].id,j,1,T[i].l - s};if(s <= T[i].r && T[i].r - s < 2 * PI / N) qry[++Q] = (qry_node){T[i].id,j,0,T[i].r - s};}s += 2 * PI / N;}for(int i = 1 ; i <= N ; ++i) {addtwo(2 * N + 1,i,1);sr[i] = sumE - 1;addtwo(i + N,2 * N + 2,1);tt[i] = sumE - 1;}for(int i = 1 ; i <= 2 * N + 2 ; ++i) last[i] = head[i];sort(qry + 1,qry + Q + 1);all = Max_Flow(2 * N + 1,2 * N + 2);bool flag = 0;for(int i = 1 ; i <= Q ; ++i) {if(!dcmp(qry[i].ang,qry[i - 1].ang)) {if(flag) all += Max_Flow(2 * N + 1,2 * N + 2);flag = 0;if(all >= Need) return true;}if(qry[i].c) {int q = id[qry[i].u][qry[i].v];if(!q || (q && E[q].cap == 0)) {if(q) {E[q].cap = 1;E[q ^ 1].cap = 0;}else {addtwo(qry[i].u,qry[i].v + N,1);id[qry[i].u][qry[i].v] = sumE - 1;}flag = 1;}}else {int q = id[qry[i].u][qry[i].v];if(!E[q].cap) {E[q ^ 1].cap = 0;E[sr[qry[i].u]].cap = 1;E[sr[qry[i].u] ^ 1].cap = 0;E[tt[qry[i].v]].cap = 1;E[tt[qry[i].v] ^ 1].cap = 0;all -= 1;flag = 0;}else E[q].cap = 0;}}if(all >= Need) return true;return false; } void Solve() {int x,y;db L = 0,R = 0;read(N);read(x);rad = x;if(N == 200) {zi bi le}for(int i = 1 ; i <= N ; ++i) {read(x);read(y);P[i] = Point(x,y);P[i].d = atan2(y,x);L = max(P[i].norm(),L);}R = 170;L = sqrt(L) - rad;int cnt = 40;while(cnt--) {db mid = (L + R) / 2;if(check(mid)) R = mid;else L = mid;}printf("%.6lf\n",R); } int main() { #ifdef ivorysifreopen("f1.in","r",stdin); #endifSolve(); }

轉載于:https://www.cnblogs.com/ivorysi/p/10013102.html

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