旋转卡壳
Sample Input
4
0 0
0 1
1 1
1 0
Sample Output
2
1 # include <iostream> 2 # include <cstdio> 3 # include <cstring> 4 # include <algorithm> 5 # include <string> 6 # include <cmath> 7 # include <queue> 8 # define LL long long 9 using namespace std ; 10 11 struct Point 12 { 13 int x,y; 14 Point(int _x = 0,int _y = 0) 15 { 16 x = _x; y = _y; 17 } 18 Point operator -(const Point &b)const 19 { 20 return Point(x - b.x, y - b.y); 21 } 22 int operator ^(const Point &b)const 23 { 24 return x*b.y - y*b.x; 25 } 26 int operator *(const Point &b)const 27 { 28 return x*b.x + y*b.y; 29 } 30 void input() 31 { 32 scanf("%d%d",&x,&y); 33 } 34 }; 35 //距离的平方 36 int dist2(Point a,Point b) 37 { 38 return (a-b)*(a-b); 39 } 40 //******二维凸包，int*********** 41 const int MAXN = 50010; 42 Point list[MAXN]; 43 int Stack[MAXN],top; 44 bool _cmp(Point p1,Point p2) 45 { 46 int tmp = (p1-list[0])^(p2-list[0]); 47 if(tmp > 0)return true; 48 else if(tmp == 0 && dist2(p1,list[0]) <= dist2(p2,list[0])) 49 return true; 50 else return false; 51 } 52 void Graham(int n) 53 { 54 Point p0; 55 int k = 0; 56 p0 = list[0]; 57 for(int i = 1;i < n;i++) 58 if(p0.y > list[i].y || (p0.y == list[i].y && p0.x > list[i].x)) 59 { 60 p0 = list[i]; 61 k = i; 62 } 63 swap(list[k],list[0]); 64 sort(list+1,list+n,_cmp); 65 if(n == 1) 66 { 67 top = 1; 68 Stack[0] = 0; 69 return; 70 } 71 if(n == 2) 72 { 73 top = 2; 74 Stack[0] = 0; Stack[1] = 1; 75 return; 76 } 77 Stack[0] = 0; Stack[1] = 1; 78 top = 2; 79 for(int i = 2;i < n;i++) 80 { 81 while(top > 1 && 82 ((list[Stack[top-1]]-list[Stack[top-2]])^(list[i]-list[Stack[top-2]])) <= 0) 83 top--; 84 Stack[top++] = i; 85 } 86 } 87 //旋转卡壳，求两点间距离平方的最大值 88 int rotating_calipers(Point p[],int n) 89 { 90 int ans = 0; 91 Point v; 92 int cur = 1; 93 for(int i = 0;i < n;i++) 94 { 95 v = p[i]-p[(i+1)%n]; 96 while((v^(p[(cur+1)%n]-p[cur])) < 0) 97 cur = (cur+1)%n; 98 ans = max(ans,max(dist2(p[i],p[cur]),dist2(p[(i+1)%n],p[(cur+1)%n]))); 99 } 100 return ans; 101 } 102 Point p[MAXN]; 103 int main() 104 { 105 //freopen("in.txt","r",stdin) ; 106 int n; 107 while(scanf("%d",&n) == 1) 108 { 109 for(int i = 0;i < n;i++) 110 list[i].input(); 111 Graham(n); 112 for(int i = 0;i < top;i++)p[i] = list[Stack[i]]; 113 printf("%d ",rotating_calipers(p,top)); 114 } 115 return 0; 116 }