HDU 4573 Throw the Stones（动态三维凸包）（2013 ACM-ICPC长沙赛区全国邀请赛）

  1 #include <cstdio>
  2 #include <algorithm>
  3 #include <iostream>
  4 #include <cstring>
  5 #include <cmath>
  6 using namespace std;
  7 typedef long long LL;
  8 
  9 const int MAXN = 10001;
 10 const double EPS = 1e-9;
 11 
 12 inline int sgn(double x) {
 13     return (x > EPS) - (x < -EPS);
 14 }
 15 
 16 struct Point {
 17     double x, y, z;
 18     Point() {}
 19     Point(double x, double y, double z): x(x), y(y), z(z) {}
 20     void read() {
 21         scanf("%lf%lf%lf", &x, &y, &z);
 22     }
 23     Point operator - (const Point &rhs) const {
 24         return Point(x - rhs.x, y - rhs.y, z - rhs.z);
 25     }
 26     double operator * (const Point &rhs) const {
 27         return x * rhs.x + y * rhs.y + z * rhs.z;
 28     }
 29 };
 30 double length(const Point &a) {
 31     return sqrt(a * a);
 32 }
 33 Point cross(const Point &a, const Point &b) {
 34     Point res;
 35     res.x = a.y * b.z - a.z * b.y;
 36     res.y = a.z * b.x - a.x * b.z;
 37     res.z = a.x * b.y - a.y * b.x;
 38     return res;
 39 }
 40 Point cross(const Point &o, const Point &a, const Point &b) {
 41     return cross(a - o, b - o);
 42 }
 43 double volume(const Point &a, const Point &b, const Point &c, const Point &d) {
 44     return cross(c - a , b - a) * (d - a) / 6;
 45 }
 46 Point p[MAXN];
 47 
 48 struct Face {
 49     int a, b, c;
 50     bool flag;
 51     Face() {}
 52     Face(int a, int b, int c, bool flag): a(a), b(b), c(c), flag(flag) {}
 53     bool can_see(const Point &q) {
 54         return sgn(volume(p[a], p[b], p[c], q)) > 0;
 55     }
 56 };
 57 Face fac[MAXN * 10];
 58 
 59 struct Convex {
 60     double diff_vol;
 61     int cnt, mat[MAXN][MAXN];
 62 
 63     void init() {
 64         cnt = 0;
 65         for(int i = 0; i < 4; ++i) {
 66             Face newf = Face((i + 1) % 4, (i + 2) % 4, (i + 3) % 4, true);
 67             if(newf.can_see(p[i])) swap(newf.a, newf.c);
 68             mat[newf.a][newf.b] = mat[newf.b][newf.c] = mat[newf.c][newf.a] = cnt;
 69             fac[cnt++] = newf;
 70         }
 71     }
 72 
 73     void restore(int k, int a, int b) {
 74         int f = mat[a][b];
 75         if(fac[f].flag) {
 76             if(fac[f].can_see(p[k])) dfs(k, f);
 77             else {
 78                 mat[b][a] = mat[a][k] = mat[k][b] = cnt;
 79                 fac[cnt++] = Face(b, a, k, true);
 80             }
 81         }
 82     }
 83 
 84     void dfs(int k, int f) {
 85         diff_vol += volume(p[fac[f].a], p[fac[f].b], p[fac[f].c], p[k]);
 86         fac[f].flag = false;
 87         restore(k, fac[f].b, fac[f].a);
 88         restore(k, fac[f].c, fac[f].b);
 89         restore(k, fac[f].a, fac[f].c);
 90     }
 91 
 92     double update(int k) {
 93         diff_vol = 0;
 94         for(int i = 0; i < cnt; ++i) {
 95             if(!fac[i].flag || !fac[i].can_see(p[k])) continue;
 96             dfs(k, i);
 97             break;
 98         }
 99         return diff_vol;
100     }
101 
102     double vol() {
103         double res = 0;
104         for(int i = 0; i < cnt; ++i) if(fac[i].flag)
105             res -= volume(p[fac[i].a], p[fac[i].b], p[fac[i].c], Point(0, 0, 0));
106         return res;
107     }
108 } solver;
109 
110 int n, kase;
111 
112 void solve() {
113     int king = 0;
114     double maxans = 0;
115     for(int i = 1, tmp = 1; i < n; ++i) {
116         if(tmp == 1) {
117             tmp += sgn(length(p[0] - p[i]));
118             if(tmp > 1) swap(p[1], p[i]);
119         } else if(tmp == 2) {
120             tmp += sgn(length(cross(p[0], p[1], p[i])));
121             if(tmp > 2) swap(p[2], p[i]);
122         } else if(tmp == 3) {
123             tmp += (sgn(volume(p[0], p[1], p[2], p[i])) != 0);
124             if(tmp > 3) {
125                 swap(p[3], p[i]);
126                 solver.init();
127                 for(int j = 4; j <= i; ++j) solver.update(j);
128                 king = i, maxans = solver.vol();
129             }
130         } else {
131             double v = solver.update(i);
132             if(sgn(v - maxans) > 0) {
133                 maxans = v;
134                 king = i;
135             }
136         }
137     }
138     printf("%d %.2f\n", king + 1, maxans);
139 }
140 
141 int main() {
142     while(scanf("%d", &n) != EOF) {
143         for(int i = 0; i < n; ++i) p[i].read();
144         printf("Case #%d:\n", ++kase);
145         solve();
146     }
147 }