矩形切割

Previous related blog: http://blog.csdn.net/lllcfr/article/details/7567045

先判断是否重叠，然后切割．注意答案要求的是哪一部分．

１． 二维矩形 USACO 5-3-window

#include <algorithm>#include <cstdio>#include <fstream>#include <iomanip>#include <list>#include <queue>#include <sstream>#include <string>using namespace std;struct Window {        char id;        int x1, x2, y1, y2;        Window(const char _id, const int _x1, const int _y1, const int _x2, const int _y2) {                id = _id;                x1 = min(_x1, _x2);                x2 = max(_x1, _x2);                y1 = min(_y1, _y2);                y2 = max(_y1, _y2);        }};int main() {ifstream fin("window.in");        ofstream fout("window.out");        list<Window> lst;        string cmd;        char id, ch;        while (fin >> cmd) {                id = cmd[2];                if (cmd[0] == 'w') {                        istringstream iss(cmd.substr(4));                        int x1, x2, y1, y2;                        iss >> x1 >> ch >> y1 >> ch >> x2 >> ch >> y2;                        lst.push_front(Window(id, x1, y1, x2, y2));                }                else if (cmd[0] == 't') {                        auto it = lst.begin();                        while (it != lst.end() && it->id != id)                                ++it;                        lst.push_front(*it);                        lst.erase(it);                }                else if (cmd[0] == 'b') {                        auto it = lst.begin();                        while (it != lst.end() && it->id != id)                                ++it;                        lst.push_back(*it);                        lst.erase(it);                }                else if (cmd[0] == 'd') {                        auto it = lst.begin();                        while (it != lst.end() && it->id != id)                                ++it;                        lst.erase(it);                }                else if (cmd[0] == 's') {                        auto it = lst.begin();                        while (it != lst.end() && it->id != id)                                ++it;                        double tot = (it->x2 - it->x1) * (it->y2 - it->y1);                        queue<Window> q;                        q.push(*it);                        for (auto jt = lst.begin(); jt != it; ++jt) {                                int n = q.size();                                while (n--) {                                        Window w = q.front();                                        q.pop();                                        if (max(w.x1, jt->x1) >= min(w.x2, jt->x2) || max(w.y1, jt->y1) >= min(w.y2, jt->y2)) {                                                q.push(w);                                                continue;                                        }                                        if (jt->x1 > w.x1) {                                                q.push(Window(0, w.x1, w.y1, jt->x1, w.y2));                                                w.x1 = jt->x1;                                        }                                        if (jt->x2 < w.x2) {                                                q.push(Window(0, jt->x2, w.y1, w.x2, w.y2));                                                w.x2 = jt->x2;                                        }                                        if (jt->y1 > w.y1) {                                                q.push(Window(0, w.x1, w.y1, w.x2, jt->y1));                                                w.y1 = jt->y1;                                        }                                        if (jt->y2 < w.y2) {                                                q.push(Window(0, w.x1, jt->y2, w.x2, w.y2));                                                w.y2 = jt->y2;                                        }                                }                        }                        double ans = 0;                        while (!q.empty()) {                                ans += (q.front().x2 - q.front().x1) * (q.front().y2 - q.front().y1);                                q.pop();                        }                        fout << fixed << setprecision(3) << ans / tot * 100 << endl;                }        }fin.close();fout.close();        //system("pause");return 0;}

２． 三维矩形 TopCoder SRM191 Div2 1000-point CuboidJoin

class CuboidJoin {        struct Cuboid {                int x1, x2, y1, y2, z1, z2;                Cuboid(int x, int y, int z, int X, int Y, int Z) {                        x1 = x, x2 = X, y1 = y, y2 = Y, z1 = z, z2 = Z;                }        };public:        long long totalVolume(vector<int> cuboids) {                vector<Cuboid> lst;                const int sz = cuboids.size();                for (int i = 0; i < sz; i += 6) {                        queue<Cuboid> q;                        q.push(Cuboid(cuboids[i], cuboids[i + 1], cuboids[i + 2],                                       cuboids[i + 3], cuboids[i + 4], cuboids[i + 5]));                        const int num = lst.size();                        for (int j = 0; j < num && !q.empty(); ++j) {                                const Cuboid const &d = lst[j];                                int n = q.size();                                while (n--) {                                        Cuboid c = q.front();                                        q.pop();                                        if (max(c.x1, d.x1) >= min(c.x2, d.x2) ||                                                max(c.y1, d.y1) >= min(c.y2, d.y2) ||                                                max(c.z1, d.z1) >= min(c.z2, d.z2)) {                                                q.push(c);                                                continue;                                        }                                        if (d.x1 > c.x1) {                                                q.push(Cuboid(c.x1, c.y1, c.z1, d.x1, c.y2, c.z2));                                                c.x1 = d.x1;                                        }                                        if (d.x2 < c.x2) {                                                q.push(Cuboid(d.x2, c.y1, c.z1, c.x2, c.y2, c.z2));                                                c.x2 = d.x2;                                        }                                        if (d.y1 > c.y1) {                                                q.push(Cuboid(c.x1, c.y1, c.z1, c.x2, d.y1, c.z2));                                                c.y1 = d.y1;                                        }                                        if (d.y2 < c.y2) {                                                q.push(Cuboid(c.x1, d.y2, c.z1, c.x2, c.y2, c.z2));                                                c.y2 = d.y2;                                        }                                        if (d.z1 > c.z1) {                                                q.push(Cuboid(c.x1, c.y1, c.z1, c.x2, c.y2, d.z1));                                                c.z1 = d.z1;                                        }                                        if (d.z2 < c.z2) {                                                q.push(Cuboid(c.x1, c.y1, d.z2, c.x2, c.y2, c.z2));                                                c.z2 = d.z2;                                        }                                }                        }                        while (!q.empty()) {                                lst.push_back(q.front());                                q.pop();                        }                }                long long ans = 0;                int k = lst.size();                for (int i = 0; i < k; ++i)                        ans += ((long long)lst[i].x2 - lst[i].x1) * ((long long)lst[i].y2 - lst[i].y1) * ((long long)lst[i].z2 - lst[i].z1);                return ans;        }};

３． 多维矩形

//toj 1074//toj 1861//usaco rect1#include <cstdio>#include <vector>#include <list>#include <algorithm>using namespace std;template<typename T>class Rect{typedef pair<T,T> segment;typedef vector<segment> space;public:void insert(const space& s){q.push_back(s);typename list<space>::iterator itr=q.end();--itr;while(q.begin()!=itr){int i;for(i=0;i<s.size();++i)if(!cross(q.front()[i],s[i]))break;if(i<s.size()){q.push_back(q.front());q.pop_front();continue;}cut(q.front(),s,s.size()-1);q.pop_front();}}T area(){T ans(0);typename list<space>::iterator itr=q.begin();for(int i=0;i<q.size();i++,itr++){T tmp=1;for(int j=0;j<itr->size();j++)tmp*=((*itr)[j].second-(*itr)[j].first);ans+=tmp;}return ans;}private:list<space> q;void cut(space& a,const space& b,int d){if(d==-1)return;space s;if(b[d].first>a[d].first){s=a;s[d].second=b[d].first;q.push_back(s);a[d].first=b[d].first;}if(b[d].second<a[d].second){s=a;s[d].first=b[d].second;q.push_back(s);a[d].second=b[d].second;}cut(a,b,d-1);}inline bool cross(segment a,segment b){return max(a.first,b.first)<min(a.second,b.second);}};int main(){int n,T=0;while(scanf("%d",&n),n){Rect<double> r;while(n--){vector<pair<double,double> > rect;double x1,y1,x2,y2;scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);rect.push_back(make_pair(x1,x2));rect.push_back(make_pair(y1,y2));r.insert(rect);}printf("Test case #%d\nTotal explored area: %.2lf\n\n",++T,r.area());}return 0;}