Given a circle with N defined points and a point M outside the circle, find the point that is closest to M among the set of N. O(LogN)

 1 // http://www.careercup.com/question?id=4877486110277632
 2 #include <cmath>
 3 #include <iostream>
 4 #include <vector>
 5 using namespace std;
 6
 7 struct Point {
 8     double x;
 9     double y;
10     Point(double _x = 0, double _y = 0): x(_x), y(_y) {};
11 };
12
13 double dist(const Point &p1, const Point &p2)
14 {
15     return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
16 }
17
18 int main()
19 {
20     int i, n;
21     Point pout;
22     vector<Point> vp;
23     int min_i;
24     double d, min_d;
25
26     while (cin >> n && n > 0) {
27         vp.resize(n);
28         for (i = 0; i < n; ++i) {
29             cin >> vp[i].x >> vp[i].y;
30         }
31         cin >> pout.x >> pout.y;
32
33         min_i = 0;
34         min_d = dist(pout, vp[0]);
35         for (i = 1; i < n; ++i) {
36             d = dist(pout, vp[i]);
37             min_i = d < min_d ? i : min_i;
38         }
39         cout << '(' << vp[min_i].x << ',' << vp[min_i].y << ')' << endl;
40         cout << min_d << endl;
41         vp.clear();
42     }
43
44     return 0;
45 }

 1 // http://www.careercup.com/question?id=4877486110277632
 2 #include <cmath>
 3 #include <iostream>
 4 #include <vector>
 5 using namespace std;
 6
 7 struct Point {
 8     double x;
 9     double y;
10     Point(double _x = 0, double _y = 0): x(_x), y(_y) {};
11
12     Point operator - (const Point &other) {
13         return Point(x - other.x, y - other.y);
14     };
15
16     Point operator + (const Point &other) {
17         return Point(x + other.x, y + other.y);
18     };
19
20     double operator * (const Point &other) {
21         return x * other.x + y * other.y;
22     };
23 };
24
25 double dist(const Point &p1, const Point &p2)
26 {
27     return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
28 }
29
30 int main()
31 {
32     int i, n;
33     Point pout;
34     vector<Point> vp;
35     Point center;
36     Point v0, vout;
37     // the angle between OM and a line of center
38     double angle;
39     // 2 * pi / n
40     double side_angle;
41     const double pi = 3.1415926;
42     double d;
43
44     while (cin >> n && n > 0) {
45         vp.resize(n);
46         for (i = 0; i < n; ++i) {
47             cin >> vp[i].x >> vp[i].y;
48
49         }
50         cin >> center.x >> center.y;
51         cin >> pout.x >> pout.y;
52
53         v0 = vp[0] - center;
54         vout = pout - center;
55
56         side_angle = 2 * pi / n;
57         angle = arccos((v0 * vout) / (dist(vp[0], center) * dist(pout, center)));
58         d = angle / side_angle;
59         // Here I assume the points are arranged in clockwise order.
60         i = d - floor(d) < 0.5 ? floor(d) : floor(d) + 1;
61         cout << vp[i].x << ' ' << vp[i].y << endl;
62
63         vp.clear();
64     }
65
66     return 0;
67 }