UVA 511 Do You Know the Way to San Jose?

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

#include <bits/stdc++.h>
using namespace std;
 
#define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define Rep(i,n) for (int i = 0; i < (n); ++i)
#define For(i,s,t) for (int i = (s); i <= (t); ++i)
#define rFor(i,t,s) for (int i = (t); i >= (s); --i)
#define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
#define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
#define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
#define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
 
#define LOWBIT(x) ((x)&(-x))
 
#define ALL(x) x.begin(),x.end()
#define INS(x) inserter(x,x.begin())
#define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
#define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 
#define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
#define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
 
#define ms0(a) memset(a,0,sizeof(a))
#define msI(a) memset(a,inf,sizeof(a))
#define msM(a) memset(a,-1,sizeof(a))

#define MP make_pair
#define PB push_back
#define ft first
#define sd second
 
template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &p) {
    in >> p.first >> p.second;
    return in;
}
 
template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
    for (auto &x: v)
        in >> x;
    return in;
}
 
template<typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
    out << "[" << p.first << ", " << p.second << "]" << "
";
    return out;
}

inline int gc(){
    static const int BUF = 1e7;
    static char buf[BUF], *bg = buf + BUF, *ed = bg;
    
    if(bg == ed) fread(bg = buf, 1, BUF, stdin);
    return *bg++;
} 

inline int ri(){
    int x = 0, f = 1, c = gc();
    for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
    for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
    return x*f;
}

template<class T>
inline string toString(T x) {
    ostringstream sout;
    sout << x;
    return sout.str();
}

inline int toInt(string s) {
    int v;
    istringstream sin(s);
    sin >> v;
    return v;
}

//min <= aim <= max
template<typename T>
inline bool BETWEEN(const T aim, const T min, const T max) {
    return min <= aim && aim <= max;
}
 
typedef long long LL;
typedef unsigned long long uLL;
typedef pair< double, double > PDD;
typedef pair< int, int > PII;
typedef pair< int, PII > PIPII;
typedef pair< string, int > PSI;
typedef pair< int, PSI > PIPSI;
typedef set< int > SI;
typedef set< PII > SPII;
typedef vector< int > VI;
typedef vector< double > VD;
typedef vector< VI > VVI;
typedef vector< SI > VSI;
typedef vector< PII > VPII;
typedef map< int, int > MII;
typedef map< int, string > MIS;
typedef map< int, PII > MIPII;
typedef map< PII, int > MPIII;
typedef map< string, int > MSI;
typedef map< string, string > MSS;
typedef map< PII, string > MPIIS;
typedef map< PII, PII > MPIIPII;
typedef multimap< int, int > MMII;
typedef multimap< string, int > MMSI;
//typedef unordered_map< int, int > uMII;
typedef pair< LL, LL > PLL;
typedef vector< LL > VL;
typedef vector< VL > VVL;
typedef priority_queue< int > PQIMax;
typedef priority_queue< int, VI, greater< int > > PQIMin;
const double EPS = 1e-8;
const LL inf = 0x7fffffff;
const LL infLL = 0x7fffffffffffffffLL;
const LL mod = 1e9 + 7;
const int maxN = 1e4 + 7;
const LL ONE = 1;
const LL evenBits = 0xaaaaaaaaaaaaaaaa;
const LL oddBits = 0x5555555555555555;

int sgn(double x) {
    if(fabs(x) < EPS) return 0;
    return x > 0 ? 1 : -1;
}

double dist(PDD a,PDD b) {
  return sqrt((a.ft - b.ft) * (a.ft - b.ft) + (a.sd - b.sd) * (a.sd - b.sd));
}

struct MAP{
    double U, D, L, R, Area, ratio; // 上下左右和面积以及长宽比 
    PDD center; // 中心点 
    string name; 
    
    MAP() {}
    MAP(string s) {
        stringstream sin(s);
        double x1, y1, x2, y2;
        
        sin >> name >> x1 >> y1 >> x2 >> y2;
        L = min(x1, x2);
        R = max(x1, x2);
        U = max(y1, y2);
        D = min(y1, y2);
        center = MP((L + R) / 2, (U + D) / 2);
        Area = (R - L) * (U - D);
        ratio = fabs((R - L) / (U - D) - 0.75);
    }
    
    bool cover(PDD x) {
        return x.ft >= L && x.ft <= R && x.sd >= D && x.sd <= U;
    }
    
    bool operator< (const MAP &x) const {
        return Area > x.Area;
    }
};
vector< MAP > maps;

string tmp; 
map< string, PDD > loc;
string target;
int level;

struct MyCmp{
    bool operator() (const MAP &x, const MAP &y) const {
        PDD tar = loc[target];
        
        if(sgn(x.Area - y.Area) == 0) {
            double a = dist(tar, x.center);
            double b = dist(tar, y.center);
            
            if(sgn(a - b) == 0) {
                if(sgn(x.ratio - y.ratio) == 0) {
                    a = dist(tar, MP(x.R, x.D));
                    b = dist(tar, MP(y.R, y.D));
                    
                    if(sgn(a - b) == 0) return x.L < y.L;
                    return a > b;
                }
                return x.ratio < y.ratio;
            }
            return a < b;
        }
        return x.Area > y.Area;
    }
}; 

int main(){
    //freopen("MyOutput.txt","w",stdout);
    //freopen("input.txt","r",stdin);
    //INIT();
    getline(cin, tmp);
    while(getline(cin, tmp)) {
        if(tmp == "LOCATIONS") break;
        maps.PB(MAP(tmp));
    }
    
    while(getline(cin, tmp)) {
        if(tmp == "REQUESTS") break;
        stringstream sin(tmp);
        double x, y;
        
        sin >> tmp >> x >> y;
        loc[tmp] = MP(x, y);
    }
    
    while(getline(cin, tmp)) {
        if(tmp == "END") break;
        stringstream sin(tmp);
        
        sin >> target >> level;
        printf("%s at detail level %d ", target.c_str(), level);
        
        if(loc.find(target) == loc.end()) printf("unknown location
");
        else {
            set< MAP, MyCmp > sm;
            // 找出所有包含target地点的map
            foreach(i, maps) if(i->cover(loc[target])) sm.insert(*i);
                
            if(sm.size() == 0) printf("no map contains that location
");
            else {
                auto it = sm.begin();
                double t = 0;
                
                while(it != sm.end()) {
                    if(it->Area != t) {
                        t = it->Area;
                        if(!--level) break;
                    }
                    ++it;
                }
                
                if(level) printf("no map at that detail level; using %s
", sm.rbegin()->name.c_str());
                else printf("using %s
", it->name.c_str());
            }
        }
    }
    return 0;
}