题目链接：https://vjudge.net/problem/UVA-511
题目翻译摘自《算法禁赛入门经典》
题目大意
有 n 张地图（已知名称和某两个对角线端点的坐标）和 m 个地名（已知名称和坐标）， 还有 q 个查询。每张地图都是边平行于坐标轴的矩形，比例定义为高度除以宽度的值。每个查询包含一个地名和详细等级 i。面积相同的地图总是属于同一个详细等级。假定包含此地名的地图中一共有 k 种不同的面积，则合法的详细等级为 1～k（其中 1 最不详细，k 最详细， 面积越小越详细）。如果详细等级 i 的地图不止一张，则输出地图中心和查询地名最接近的一张；如果还有并列的，地图长宽比应尽量接近 0.75（这是Web浏览器的比例）；如果还有并列，查询地名和地图右下角的坐标应最远（对应最少的滚动条移动）；如果还有并列，则输出x坐标最小的一个。如果查询的地名不存在或者没有地图包含它，应报告查询非法。如果包含它的地图最高详细等级小于 i，应报告查询非法（并输出包含它的最详细地图名称，如果存在）。
分析
对于每个询问，找出所有相关区域，然后用自定义比较器排一下序即可。
代码如下
1 #include <bits/stdc++.h> 2 using namespace std; 3 4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); 5 #define Rep(i,n) for (int i = 0; i < (n); ++i) 6 #define For(i,s,t) for (int i = (s); i <= (t); ++i) 7 #define rFor(i,t,s) for (int i = (t); i >= (s); --i) 8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i) 9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i) 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i) 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i) 12 13 #define pr(x) cout << #x << " = " << x << " " 14 #define prln(x) cout << #x << " = " << x << endl 15 16 #define LOWBIT(x) ((x)&(-x)) 17 18 #define ALL(x) x.begin(),x.end() 19 #define INS(x) inserter(x,x.begin()) 20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end()) 21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 22 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower); 23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper); 24 25 #define ms0(a) memset(a,0,sizeof(a)) 26 #define msI(a) memset(a,inf,sizeof(a)) 27 #define msM(a) memset(a,-1,sizeof(a)) 28 29 #define MP make_pair 30 #define PB push_back 31 #define ft first 32 #define sd second 33 34 template<typename T1, typename T2> 35 istream &operator>>(istream &in, pair<T1, T2> &p) { 36 in >> p.first >> p.second; 37 return in; 38 } 39 40 template<typename T> 41 istream &operator>>(istream &in, vector<T> &v) { 42 for (auto &x: v) 43 in >> x; 44 return in; 45 } 46 47 template<typename T1, typename T2> 48 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) { 49 out << "[" << p.first << ", " << p.second << "]" << "\n"; 50 return out; 51 } 52 53 inline int gc(){ 54 static const int BUF = 1e7; 55 static char buf[BUF], *bg = buf + BUF, *ed = bg; 56 57 if(bg == ed) fread(bg = buf, 1, BUF, stdin); 58 return *bg++; 59 } 60 61 inline int ri(){ 62 int x = 0, f = 1, c = gc(); 63 for(; c<48||c>57; f = c=='-'?-1:f, c=gc()); 64 for(; c>47&&c<58; x = x*10 + c - 48, c=gc()); 65 return x*f; 66 } 67 68 template<class T> 69 inline string toString(T x) { 70 ostringstream sout; 71 sout << x; 72 return sout.str(); 73 } 74 75 inline int toInt(string s) { 76 int v; 77 istringstream sin(s); 78 sin >> v; 79 return v; 80 } 81 82 //min <= aim <= max 83 template<typename T> 84 inline bool BETWEEN(const T aim, const T min, const T max) { 85 return min <= aim && aim <= max; 86 } 87 88 typedef long long LL; 89 typedef unsigned long long uLL; 90 typedef pair< double, double > PDD; 91 typedef pair< int, int > PII; 92 typedef pair< int, PII > PIPII; 93 typedef pair< string, int > PSI; 94 typedef pair< int, PSI > PIPSI; 95 typedef set< int > SI; 96 typedef set< PII > SPII; 97 typedef vector< int > VI; 98 typedef vector< double > VD; 99 typedef vector< VI > VVI; 100 typedef vector< SI > VSI; 101 typedef vector< PII > VPII; 102 typedef map< int, int > MII; 103 typedef map< int, string > MIS; 104 typedef map< int, PII > MIPII; 105 typedef map< PII, int > MPIII; 106 typedef map< string, int > MSI; 107 typedef map< string, string > MSS; 108 typedef map< PII, string > MPIIS; 109 typedef map< PII, PII > MPIIPII; 110 typedef multimap< int, int > MMII; 111 typedef multimap< string, int > MMSI; 112 //typedef unordered_map< int, int > uMII; 113 typedef pair< LL, LL > PLL; 114 typedef vector< LL > VL; 115 typedef vector< VL > VVL; 116 typedef priority_queue< int > PQIMax; 117 typedef priority_queue< int, VI, greater< int > > PQIMin; 118 const double EPS = 1e-8; 119 const LL inf = 0x7fffffff; 120 const LL infLL = 0x7fffffffffffffffLL; 121 const LL mod = 1e9 + 7; 122 const int maxN = 1e4 + 7; 123 const LL ONE = 1; 124 const LL evenBits = 0xaaaaaaaaaaaaaaaa; 125 const LL oddBits = 0x5555555555555555; 126 127 int sgn(double x) { 128 if(fabs(x) < EPS) return 0; 129 return x > 0 ? 1 : -1; 130 } 131 132 double dist(PDD a,PDD b) { 133 return sqrt((a.ft - b.ft) * (a.ft - b.ft) + (a.sd - b.sd) * (a.sd - b.sd)); 134 } 135 136 struct MAP{ 137 double U, D, L, R, Area, ratio; // 上下左右和面积以及长宽比 138 PDD center; // 中心点 139 string name; 140 141 MAP() {} 142 MAP(string s) { 143 stringstream sin(s); 144 double x1, y1, x2, y2; 145 146 sin >> name >> x1 >> y1 >> x2 >> y2; 147 L = min(x1, x2); 148 R = max(x1, x2); 149 U = max(y1, y2); 150 D = min(y1, y2); 151 center = MP((L + R) / 2, (U + D) / 2); 152 Area = (R - L) * (U - D); 153 ratio = fabs((R - L) / (U - D) - 0.75); 154 } 155 156 bool cover(PDD x) { 157 return x.ft >= L && x.ft <= R && x.sd >= D && x.sd <= U; 158 } 159 160 bool operator< (const MAP &x) const { 161 return Area > x.Area; 162 } 163 }; 164 vector< MAP > maps; 165 166 string tmp; 167 map< string, PDD > loc; 168 string target; 169 int level; 170 171 struct MyCmp{ 172 bool operator() (const MAP &x, const MAP &y) const { 173 PDD tar = loc[target]; 174 175 if(sgn(x.Area - y.Area) == 0) { 176 double a = dist(tar, x.center); 177 double b = dist(tar, y.center); 178 179 if(sgn(a - b) == 0) { 180 if(sgn(x.ratio - y.ratio) == 0) { 181 a = dist(tar, MP(x.R, x.D)); 182 b = dist(tar, MP(y.R, y.D)); 183 184 if(sgn(a - b) == 0) return x.L < y.L; 185 return a > b; 186 } 187 return x.ratio < y.ratio; 188 } 189 return a < b; 190 } 191 return x.Area > y.Area; 192 } 193 }; 194 195 int main(){ 196 //freopen("MyOutput.txt","w",stdout); 197 //freopen("input.txt","r",stdin); 198 //INIT(); 199 getline(cin, tmp); 200 while(getline(cin, tmp)) { 201 if(tmp == "LOCATIONS") break; 202 maps.PB(MAP(tmp)); 203 } 204 205 while(getline(cin, tmp)) { 206 if(tmp == "REQUESTS") break; 207 stringstream sin(tmp); 208 double x, y; 209 210 sin >> tmp >> x >> y; 211 loc[tmp] = MP(x, y); 212 } 213 214 while(getline(cin, tmp)) { 215 if(tmp == "END") break; 216 stringstream sin(tmp); 217 218 sin >> target >> level; 219 printf("%s at detail level %d ", target.c_str(), level); 220 221 if(loc.find(target) == loc.end()) printf("unknown location\n"); 222 else { 223 set< MAP, MyCmp > sm; 224 // 找出所有包含target地点的map 225 foreach(i, maps) if(i->cover(loc[target])) sm.insert(*i); 226 227 if(sm.size() == 0) printf("no map contains that location\n"); 228 else { 229 auto it = sm.begin(); 230 double t = 0; 231 232 while(it != sm.end()) { 233 if(it->Area != t) { 234 t = it->Area; 235 if(!--level) break; 236 } 237 ++it; 238 } 239 240 if(level) printf("no map at that detail level; using %s\n", sm.rbegin()->name.c_str()); 241 else printf("using %s\n", it->name.c_str()); 242 } 243 } 244 } 245 return 0; 246 }