离散化解矩形覆盖

神马是离散化：http://www.matrix67.com/blog/archives/108

例题：POJ 1151 Atlantis

#include <iostream>

#include <vector>

#include <set>

#include <algorithm>

#include <iomanip>

using namespace std;

struct rect

{

    double x1;

    double x2;

    double y1;

    double y2;

};

int main(int argc, char **argv)

{

    int t = 1;

    int n;

    while (cin >> n && n)

    {

        vector<double> vecX, vecY;

        vector<rect> vecRec;

        set<pair<double, double> > setCover;

        // Insert x, y to vecX, vecY.

        while (n--)

        {

            rect r;

            cin >> r.x1 >> r.y1 >> r.x2 >> r.y2;

            vecX.push_back(r.x1);

            vecX.push_back(r.x2);

            vecY.push_back(r.y1);

            vecY.push_back(r.y2);

            vecRec.push_back(r);

        }

        // Sort

        sort(vecX.begin(), vecX.end());

        sort(vecY.begin(), vecY.end());

        // Mark cover

        for (vector<rect>::const_iterator it = vecRec.begin();

            it != vecRec.end();

            ++it)

        {

            vector<double>::iterator x1 = lower_bound(vecX.begin(), vecX.end(), it->x1);

            vector<double>::iterator x2 = lower_bound(vecX.begin(), vecX.end(), it->x2);

            vector<double>::iterator y1 = lower_bound(vecY.begin(), vecY.end(), it->y1);

            vector<double>::iterator y2 = lower_bound(vecY.begin(), vecY.end(), it->y2);

            for (vector<double>::iterator x = x1; x != x2; ++x)

            {

                for (vector<double>::iterator y = y1; y != y2; ++y)

                {

                    setCover.insert(make_pair(*x, *y));

                }

            }

        }

        double sum = 0.0;

        // Calculate result

        for (vector<double>::const_iterator x = vecX.begin(); x != vecX.end() - 1; ++x)

        {

            for (vector<double>::const_iterator y = vecY.begin(); y != vecY.end() - 1; ++y)

            {

                if (setCover.find(make_pair(*x, *y)) != setCover.end())

                {

                    sum += (*(x + 1) - *x) * (*(y + 1) - *y);

                }

            }

        }

        // Make sure output format is correct.

        cout << "Test case #" << t++ << endl;

        cout << "Total explored area: " << setprecision(2) << fixed << sum << endl;

        cout << endl;

    }

    return 0;

}