Codechef 13.11QPOINT 扫描线+可持久化平衡树
题目大意就是在平面上给定若干个简单多边形，保证任意两个多边形都没有交点。
每次给定一个点询问这个点在哪个多边形中，或者返回这个点不在任何一个多边形中。
算法当然和平面图是一个算法咯。
但是有细节上的不同：
多边形边上的点也算是多边形里面的点。
就这点细节卡了我一个星期。。。
你问我什么细节？我才不会告诉你呢！
算我良心发现，放一份能ac的代码吧。
详情请参考我的第一轮集训队作业题解。
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 | #include <cstdio>#include <vector>#include <cstdlib>#include <cstring>#include <iostream>#include <algorithm>using namespace std;#define N 300010typedef long long ll;typedef long double db;static const db eps = 1e-8;int getint(){ int c; while(!isdigit(c = getchar())); int x = c - '0'; while(isdigit(c = getchar())) }struct Point{ int x, y; Point(){} Point(int _x, int _y): x(_x), y(_y){}};ll cross(const Point &a, const Point &b){ return (ll)a.x * b.y - (ll)a.y * b.x;}struct Segment{ Point l, r; int down, bel; Segment(){} Segment(Point _l, Point _r, int _down, int _bel): l(_l), r(_r), down(_down), bel(_bel){} db gety(db x){ return l.y + (db)(r.y - l.y) / (r.x - l.x) * (x - l.x); } bool on(Point p){ if(p.x < l.x || p.x > r.x) return 0; return (ll)(p.y - l.y) * (r.x - l.x) == (ll)(r.y - l.y) * (p.x - l.x); }}S[N];int num;#define ls ch[0]#define rs ch[1]struct Node{ Node *ch[2]; int size, id, p; Node(): size(0){} void up(){ size = ls -> size + rs -> size + 1; }}mem[15000010], *P = mem, Tnull, *null = &Tnull;Node *newnode(){ P -> ls = P -> rs = null; P -> size = 1; P -> p = rand(); return P++;}void copy(Node *&x, Node *y){ if(y == null) x = null; else *(x = newnode()) = *y;}void Merge(Node *&re, Node *x, Node *y){ if(x == null) copy(re, y); else if(y == null) copy(re, x); else if(x -> p < y -> p){ copy(re, x); Merge(re -> rs, x -> rs, y); re -> up(); } else{ copy(re, y); Merge(re -> ls, x, y -> ls); re -> up(); }}void Split(Node *p, Node *&x, Node *&y, int k){ if(k == 0){ copy(x, null); copy(y, p); } else if(k == p -> size){ copy(x, p); copy(y, null); } else if(k <= p -> ls -> size){ copy(y, p); Split(p -> ls, x, y -> ls, k); y -> up(); } else{ copy(x, p); Split(p -> rs, x -> rs, y, k - p -> ls -> size -1); x -> up(); }}Node *find_succ(Node *p, db _x, db _y){ if(p == null) return null; db y = S[p -> id].gety(_x); if(y + eps >= _y){ Node *temp = find_succ(p -> ls, _x, _y); return temp == null ? p : temp; } else return find_succ(p -> rs, _x, _y);}int calc_down(Node *p, db _x, int id){ if(p == null) return 0; if(S[id].gety(_x) <= S[p -> id].gety(_x)) return calc_down(p -> ls, _x, id); else return p -> ls -> size + 1 + calc_down(p -> rs, _x, id);}Node *insert(Node *p, db _x, int id){ int down = calc_down(p, _x, id); Node *x, *y, *re; Split(p, x, y, down); Node *now = newnode(); now -> id = id; Merge(re, x, now); Merge(re, re, y); return re;}Node *cutoff(Node *p, db _x, int id){ int down = calc_down(p, _x, id); Node *x, *y, *z, *re; Split(p, x, y, down); Split(y, y, z, 1); Merge(re, x, z); return re;}Point p[N];int ux[N];vector<int>in[N], out[N];Node *root[N];int get_ins(Node *p, int x, int y){ static Node *temp; temp = find_succ(p, x, y); if(temp == null) return -1; else if(S[temp -> id].on(Point(x, y))) return S[temp -> id].bel; else return S[temp -> id].down;}int main(){#ifndef ONLINE_JUDGE //freopen("tt.in", "r", stdin); //freopen("tt.out", "w", stdout);#endif int n, i, j, t, m = 0; scanf("%d", &n); for(i = 1; i <= n; ++i){ scanf("%d", &t); for(j = 1; j <= t; ++j){ scanf("%d%d", &p[j].x, &p[j].y); ux[++m] = p[j].x; } p[t + 1] = p[1]; ll area = 0; for(j = 1; j <= t; ++j) area += cross(p[j], p[j + 1]); if(area < 0){ for(j = 1; j <= t; ++j){ if(p[j].x < p[j + 1].x) S[++num] = Segment(p[j], p[j + 1], i, i); else if(p[j + 1].x < p[j].x) S[++num] = Segment(p[j + 1], p[j], -1, i); } } else{ for(j = 1; j <= t; ++j){ if(p[j].x < p[j + 1].x) S[++num] = Segment(p[j], p[j +1], -1, i); else if(p[j + 1].x < p[j].x) S[++num] = Segment(p[j +1], p[j], i, i); } } } sort(ux + 1, ux + m + 1); int _m = unique(ux + 1, ux + m + 1) - ux - 1; for(i = 1; i <= num; ++i){ in[lower_bound(ux + 1, ux + _m + 1, S[i].l.x) - ux].push_back(i); out[lower_bound(ux + 1, ux + _m + 1, S[i].r.x) - ux].push_back(i); } for(root[0] = null, i = 1; i <= _m; ++i){ root[i] = root[i - 1]; for(j = 0; j < out[i].size(); ++j) root[i] = cutoff(root[i], .5 * (ux[i] + ux[i - 1]), out[i][j]); for(j = 0; j < in[i].size(); ++j) root[i] = insert(root[i], .5 * (ux[i] + ux[i + 1]), in[i][j]); } //printf("%d\n", P - mem); int q, x, y, ans, ins; scanf("%d", &q); for(i = 1; i <= q; ++i){ //printf("%d\n", i); scanf("%d%d", &x, &y); if(x < ux[1] || x > ux[_m]) ans = -1; else{ ins = lower_bound(ux + 1, ux + _m + 1, x) - ux; if(ux[ins] == x) ans = max(get_ins(root[ins - 1], x, y), get_ins(root[ins], x, y)); else ans = get_ins(root[ins - 1], x, y); } printf("%d\n", ans); fflush(stdout); } return 0;} |
9 个月前
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