Codeforces Round #346 (Div. 2)(D)计算几何
来源:互联网 发布:win7上安装ubuntu系统 编辑:程序博客网 时间:2024/04/29 08:57
Maria participates in a bicycle race.
The speedway takes place on the shores of Lake Lucerne, just repeating its contour. As you know, the lake shore consists only of straight sections, directed to the north, south, east or west.
Let's introduce a system of coordinates, directing the Ox axis from west to east, and the Oy axis from south to north. As a starting position of the race the southernmost point of the track is selected (and if there are several such points, the most western among them). The participants start the race, moving to the north. At all straight sections of the track, the participants travel in one of the four directions (north, south, east or west) and change the direction of movement only in bends between the straight sections. The participants, of course, never turn back, that is, they do not change the direction of movement from north to south or from east to west (or vice versa).
Maria is still young, so she does not feel confident at some turns. Namely, Maria feels insecure if at a failed or untimely turn, she gets into the water. In other words, Maria considers the turn dangerous if she immediately gets into the water if it is ignored.
Help Maria get ready for the competition — determine the number of dangerous turns on the track.
The first line of the input contains an integer n (4 ≤ n ≤ 1000) — the number of straight sections of the track.
The following (n + 1)-th line contains pairs of integers (xi, yi) ( - 10 000 ≤ xi, yi ≤ 10 000). The first of these points is the starting position. The i-th straight section of the track begins at the point (xi, yi) and ends at the point(xi + 1, yi + 1).
It is guaranteed that:
- the first straight section is directed to the north;
- the southernmost (and if there are several, then the most western of among them) point of the track is the first point;
- the last point coincides with the first one (i.e., the start position);
- any pair of straight sections of the track has no shared points (except for the neighboring ones, they share exactly one point);
- no pair of points (except for the first and last one) is the same;
- no two adjacent straight sections are directed in the same direction or in opposite directions.
Print a single integer — the number of dangerous turns on the track.
60 00 11 11 22 22 00 0
1
161 11 53 53 72 72 96 96 75 75 34 34 43 43 25 25 11 1
6
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:问人在骑车的时候会不会拐进多边形里面
题解:查了一下题解,这一题使用叉积去做,(并不是很懂),通过判断向量的正负来判断拐弯的方向,而判断危险的拐点
#include<cstdio> #include<cstring> #include<cstdlib> #include<cmath> #include<iostream> #include<algorithm> #include<vector> #include<map> #include<set> #include<queue> #include<string> #include<bitset> #include<utility> #include<functional> #include<iomanip> #include<sstream> #include<ctime> using namespace std;#define N int(1e4+10) #define inf int(0x3f3f3f3f) #define mod int(1e9+7) typedef long long LL;vector<pair<int, int> >v;typedef pair<int, int> pp;bool check(pp &A, pp& B, pp& C){return (B.first - A.first)*(C.second - B.second) - (C.first - B.first)*(B.second - A.second)>0;}int main(){#ifdef CDZSC freopen("i.txt", "r", stdin);//freopen("o.txt","w",stdout); int _time_jc = clock();#endif int n,x,y;while (~scanf("%d", &n)){int ans = 0;v.clear();for (int i = 0; i <n+1; i++){scanf("%d%d", &x, &y);v.push_back(make_pair(x, y));}for (int i = 2; i <n+1; i++){if (check(v[i - 2], v[i - 1], v[i]))ans++;}printf("%d\n", ans);}return 0;}
- Codeforces Round #346 (Div. 2)(D)计算几何
- Codeforces Round #340 (Div. 2) D. Polyline 计算几何,折线
- Codeforces Round #409Div.2D. Volatile Kite(计算几何)
- Codeforces Round #409 (rated, Div. 2, based on VK Cup 2017 Round 2) D (简单计算几何)
- Codeforces Round #409 (Div. 2) D. Volatile Kite 计算几何、凸多边形、线段类
- 【计算几何】Codeforces Round #113 (Div. 2)-B. Polygons
- Codeforces Round #357 (Div. 2) E 计算几何
- Codeforces Round #365 (Div. 2) C 计算几何
- Codeforces Round #445 Div1 D:Symmetric Projections (计算几何)
- Educational Codeforces Round 11 D 计算几何
- Codeforces Round #291 (Div. 2) -- B. Han Solo and Lazer Gun (计算几何~暴力)
- Codeforces Round #365 (Div. 2) C. Chris and Road(计算几何+二分)
- Codeforces Round #365 (Div. 2) C. Chris and Road(计算几何+二分)
- codeforces Round # 187(Div.2) D
- Codeforces Round #277 (Div. 2)(D)
- Codeforces Round #291 (Div. 2)(D)
- Codeforces Round #346 (Div. 2) easy(A-D)
- Codeforces Round #346 (Div. 2) D (叉积)
- 教会你Linux Shell自动交互的三种方法
- 【Google Code Jam】Problem A. Store Credit
- LED灯的任意操纵
- git 搭建服务器
- 【Unity3D游戏开发】性能优化之如何将包大小减少到极致(三六)
- Codeforces Round #346 (Div. 2)(D)计算几何
- 8628 相亲
- 算法训练 区间k大数查询
- hdu4542 求反素数
- UVa 10763 - Foreign Exchange
- 使用Cocoapods管理framework
- 5. Longest Palindromic Substring
- iOS岗位面试一及小结
- 【Unity3D游戏开发】性能优化之Texture图片空间和内存占用分析(三七)