Careercup

2014-05-10 22:58

题目链接

原题：

Three points are given A(x1, y1), B(x2, y2), C(x3, y3). Write a method returning an array of points (x, y) inside the triangle ABC.

题目：给定三个点，找出所有这三点组成的三角形内的整点。(不能组成三角形也无所谓，结果为空即可。)

解法：出题者没有说是整点，但如果不是整点，就有无穷多个了。求整点的个数可以用Pick定律的公式。要求出所有整点的话，我的方法是找出一个内部的整点，然后向四个方向进行DFS，直到找出所有点。搜索过程中，需要判断点是否在三角形内部。我的判断方法是计算面积。对于整数问题，计算公式不要引入浮点数，误差是不必要的。所以海伦公式不可行，用行列式计算面积更为方便、准确。

代码：

// http://www.careercup.com/question?id=5120588943196160
#include <iostream>
#include <unordered_set>
#include <vector>
using namespace std;

struct Point {
    int x;
    int y;
    Point(int _x = 0, int _y = 0): x(_x), y(_y) {};
};

struct hashFunctor {
    size_t operator () (const Point &p) {
        return p.x * 10000 + p.y;
    };
};

struct equalFunctor {
    bool operator () (const Point &p1, const Point &p2) {
        return p1.x == p2.x && p1.y == p2.y;
    };
};

typedef unordered_set<Point, hashFunctor, equalFunctor> point_set;

int twoArea(int x1, int y1, int x2, int y2, int x3, int y3)
{
    return abs(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2));
}

bool inside(int x[3], int y[3], int px, int py)
{
    int sum = 0;
    
    sum += twoArea(x[0], y[0], x[1], y[1], px, py);
    sum += twoArea(x[1], y[1], x[2], y[2], px, py);
    sum += twoArea(x[2], y[2], x[0], y[0], px, py);
    return sum == twoArea(x[0], y[0], x[1], y[1], x[2], y[2]);
}

void DFS(int x[3], int y[3], int px, int py, point_set &um, point_set &visited)
{
    static const int dir[4][2] = {
        {-1, 0}, 
        {+1, 0}, 
        {0, -1}, 
        {0, +1}
    };
    int i;
    int newx, newy;
    
    visited.insert(Point(px, py));
    um.insert(Point(px, py));
    
    for (i = 0; i < 4; ++i) {
        newx = px + dir[i][0];
        newy = py + dir[i][1];
        if (visited.find(Point(newx, newy)) == visited.end() && 
            inside(x, y, newx, newy)) {
            DFS(x, y, newx, newy, um, visited);
        }
    }
}

void insidePoints(int x[3], int y[3], vector<Point> &points)
{
    point_set um;
    point_set visited;
    int mx, my;
    
    mx = (x[0] + x[1] + x[2]) / 3;
    my = (y[0] + y[1] + y[2]) / 3;
    DFS(x, y, mx, my, um, visited);
    
    point_set::const_iterator usit;
    for (usit = um.begin(); usit != um.end(); ++usit) {
        points.push_back(Point(usit->x, usit->y));
    }
    um.clear();
    visited.clear();
}

int main()
{
    int x[3];
    int y[3];
    vector<Point> points;
    int i;
    int n;
    
    while (cin >> x[0] >> y[0]) {
        cin >> x[1] >> y[1];
        cin >> x[2] >> y[2];
        insidePoints(x, y, points);
        n = (int)points.size();
        for (i = 0; i < n; ++i) {
            cout << points[i].x << ' ' << points[i].y << endl;
        }
        points.clear();
    }
    
    return 0;
}