poj2187
凸包求直径（socalled。。）
采用Graham+Rotating_Calipers，Graham复杂度nlogn，RC算法复杂度n，所以时间复杂度不会很高。
学习RC算法，可到http://cgm.cs.mcgill.ca/~orm/rotcal.frame.html。
另：http://www.cppblog.com/staryjy/archive/2009/11/19/101412.html
另外，Graham的过程即将整理。。
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#include <iostream> #include <math.h> #include <algorithm> using namespace std; #define eps 1e-8 #define zero(x) (((x)>0?(x):-(x))<eps) struct point{ double x, y; }p[50005], convex[50005]; double xmult(point p1, point p2, point p0) { return (p1.x - p0.x)*(p2.y - p0.y) - (p2.x - p0.x)*(p1.y - p0.y); } int dist2(point a, point b) { return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y); } point p1, p2; int graham_cp(const void* a, const void* b){ double ret = xmult(*((point*)a), *((point*)b), p1); return zero(ret) ? (xmult(*((point*)a), *((point*)b), p2) > 0 ? 1 : -1) : (ret > 0 ? 1 : -1); } void _graham(int n, point* p, int& s, point* ch){ int i, k = 0; for (p1 = p2 = p[0], i = 1; i<n; p2.x += p[i].x, p2.y += p[i].y, i++) if (p1.y - p[i].y>eps || (zero(p1.y - p[i].y) && p1.x > p[i].x)) p1 = p[k = i]; p2.x /= n, p2.y /= n; p[k] = p[0], p[0] = p1; qsort(p + 1, n - 1, sizeof(point), graham_cp); for (ch[0] = p[0], ch[1] = p[1], ch[2] = p[2], s = i = 3; i < n; ch[s++] = p[i++]) for (; s>2 && xmult(ch[s - 2], p[i], ch[s - 1]) < -eps; s--); } int wipesame_cp(const void *a, const void *b) { if ((*(point *)a).y < (*(point *)b).y - eps) return -1; else if ((*(point *)a).y >(*(point *)b).y + eps) return 1; else if ((*(point *)a).x < (*(point *)b).x - eps) return -1; else if ((*(point *)a).x >(*(point *)b).x + eps) return 1; else return 0; } int _wipesame(point * p, int n) { int i, k; qsort(p, n, sizeof(point), wipesame_cp); for (k = i = 1; i < n; i++) if (wipesame_cp(p + i, p + i - 1) != 0) p[k++] = p[i]; return k; } int graham(int n, point* p, point* convex, int maxsize = 1, int dir = 1){ point* temp = new point[n]; int s, i; n = _wipesame(p, n); _graham(n, p, s, temp); for (convex[0] = temp[0], n = 1, i = (dir ? 1 : (s - 1)); dir ? (i < s) : i; i += (dir ? 1 : -1)) if (maxsize || !zero(xmult(temp[i - 1], temp[i], temp[(i + 1) % s]))) convex[n++] = temp[i]; delete[]temp; return n; } int rotating_calipers(point *ch, int n) { int q = 1, ans = 0; ch[n] = ch[0]; for (int p = 0; p < n; p++) { while (xmult(ch[p + 1], ch[q + 1], ch[p]) > xmult(ch[p + 1], ch[q], ch[p])) q = (q + 1) % n; ans = max(ans, max(dist2(ch[p], ch[q]), dist2(ch[p + 1], ch[q + 1]))); } return ans; } int main() { int n; cin >> n; for (int i = 0; i < n; i++) { scanf("%lf%lf", &p[i].x, &p[i].y); } int size = graham(n, p, convex, 1, 0); cout << rotating_calipers(convex, size) << endl; return 0; } |