pku 2187(最远点对，旋转卡壳)

 1 #include <cstdio>

 2 #include <cstdlib>

 3 #include <iostream>

 4 

 5 using namespace std;

 6 

 7 const int N = 50005;

 8 

 9 //旋转卡壳(变化)求凸包直径O(n)

10 struct point {

11     int x, y;

12 }p[N];

13 

14 int dis(point A, point B) {

15     return (A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y);

16 }

17 

18 int crossProd(point A, point B, point C) {

19     return (B.x - A.x) * (C.y - A.y) - (B.y - A.y) * (C.x - A.x); 

20 }

21 

22 int cmp(const void *a, const void *b) {

23     point *c = (point *)a;

24     point *d = (point *)b;

25     int k = crossProd(p[0], *c, *d);

26     if (k<0 || !k&&dis(p[0], *c)>dis(p[0], *d)) return 1;

27     return -1;

28 }

29 

30 //计算凸包，输入点集p，点的个数n，输出凸包的顶点个数 

31 int Graham(point *p, int n) {

32     int x = p[0].x;

33     int y = p[0].y;

34     int mi = 0;

35     for (int i=1; i<n; ++i) {

36         if (p[i].y<y || p[i].y==y&&p[i].x<x) {

37             x = p[i].x;

38             y = p[i].y;

39             mi = i;

40         }

41     }

42     point tmp = p[0];

43     p[0] = p[mi];

44     p[mi] = tmp;

45     qsort(p+1, n-1, sizeof(point), cmp);

46     int top = 1;

47     for (int i=2; i<n; ++i) {

48         while (crossProd(p[top-1], p[top], p[i])<=0 && top>=1) --top;

49         p[++top] = p[i];

50     }

51     return top + 1;

52 }

53 

54 //计算凸包直径，输入凸包ch，顶点个数为n，按逆时针排列，输出直径的平方

55 int rotating_calipers(point *ch, int n) {

56     int q = 1, ans = 0;

57     ch[n] = ch[0];

58     for (int i=0; i<n; ++i) {

59         while (crossProd(ch[i+1], ch[q+1], ch[i]) > crossProd(ch[i+1], ch[q], ch[i])) q = (q + 1) % n;

60         ans = max(ans, max(dis(ch[i+1], ch[q+1]), dis(ch[i], ch[q])));

61     }

62     return ans;

63 }

64 

65 int main() {

66     int n;

67     while (scanf("%d", &n) != EOF) {

68         for (int i=0; i<n; ++i) scanf ("%d%d", &p[i].x, &p[i].y);

69         int top = Graham(p, n);

70         int ans = rotating_calipers(p, top);

71         printf ("%d\n", ans);

72     }

73     return 0;

74 }