Codeforces Round #346 (Div. 2) D Bicycle Race （叉积）

Note

The first sample corresponds to the picture:

The picture shows that you can get in the water under unfortunate circumstances only at turn at the point (1, 1). Thus, the answer is 1.

题意：给出一个多边形的所有点坐标（按顺序给），某人求顺时针走一圈有多少条边使他走进多边形内。

分析：这个人在顺时针走，如果连着的两条线段，是逆时针的，显然这个人就走到多边形内部去了

这个就用个叉积去判一判就好了。

#include <cstdio>#include <cstring>#include <stack>#include <queue>#include <map>#include <set>#include <vector>#include <cmath>#include <algorithm>using namespace std;const double eps = 1e-6;const double pi = acos(-1.0);const int INF = 0x3f3f3f3f;const int MOD = 1000000007;#define ll long long#define CL(a,b) memset(a,b,sizeof(a))#define lson (i<<1)#define rson ((i<<1)|1)#define MAXN 100010struct node{    int x,y;}s[1010];int chaji(node A, node B, node C){    return (A.x-B.x)*(C.y-B.y)-(C.x-B.x)*(A.y-B.y);}int main(){    int n;    while(scanf("%d",&n)==1)    {        for(int i=0; i<=n; i++)            cin>>s[i].x>>s[i].y;        s[n+1].x = s[1].x;        s[n+1].y = s[1].y;        int ans = 0;        for(int i=1; i<=n; i++)        {            if(chaji(s[i-1], s[i], s[i+1]) < 0)                ans++;        }        cout<<ans<<endl;    }    return 0;}