题意: 平面上有n个端点的一笔画,最后一个端点与第一个端点重合,即所给图案是闭合曲线.求这些线段将平面分成多少部分. 分析: 平面图中欧拉定理:设平面的顶点数.边数和面数分别为V.E和F.则 V+F-E=2 所求结果不容易直接求出,因此我们可以转换成 F=E-V+2 枚举两条边,如果有交点则顶点数+1,并将交点记录下来 所有交点去重(去重前记得排序),如果某个交点在线段上,则边数+1 //#define LOCAL #include <cstdio> #include <cstring&…

That Nice Euler Circuit Little Joey invented a scrabble machine that he called Euler, after the great mathematician. In his primary school Joey heard about the nice story of how Euler started the study about graphs. The problem in that story was - le…

UVALive - 3263 That Nice Euler Circuit (几何) ACM 题目地址:  UVALive - 3263 That Nice Euler Circuit 题意:  给出一个点,问连起来后的图形把平面分为几个区域. 分析:  欧拉定理有:设平面图的顶点数.边数.面数分别V,E,F则V+F-E=2  大白的题目,做起来还是非常有技巧的. 代码: /* * Author: illuz <iilluzen[at]gmail.com> * File: LA3263.cp…

That Nice Euler Circuit [题目链接]That Nice Euler Circuit [题目类型]几何 &题解: 蓝书P260 要用欧拉定理:V+F=E+2 V是顶点数;F是分成了多少区域,也就是本题的答案;E是有多少条边,比如2条线段相交,就有4条边,而不是2条. 还有几点注意: 1.dcmp()没有返回0 调了半天(模板照着敲都能错 0.0!) 2.V[]点没有去重 wa了1次(这个去重还是很难想的,去重之后还要证出原来的方法是正确的) 还有他这种算E(边数)的想法很好…

Little Joey invented a scrabble machine that he called Euler, after the great mathematician. In his primary school Joey heard about the nice story of how Euler started the study about graphs. The problem in that story was - let me remind you - to dra…

题目链接:poj2284 That Nice Euler Circuit 欧拉公式:如果G是一个阶为n,边数为m且含有r个区域的连通平面图,则有恒等式:n-m+r=2. 欧拉公式的推广: 对于具有k(k≥2)个连通分支的平面图G,有:n-m+r=k+1. 题意:给出连通平面图的各顶点,求这个欧拉回路将平面分成多少区域. 题解:根据平面图的欧拉定理“n-m+r=2”来求解区域数r. 顶点个数n:两两线段求交点,每个交点都是图中的顶点. 边数m:在求交点时判断每个交点落在第几条边上,如果一个交点落在…

                                                      That Nice Euler Circuit Time Limit: 3000MS   Memory Limit: 65536K Total Submissions: 1977   Accepted: 626 Description Little Joey invented a scrabble machine that he called Euler, after the great…

That Nice Euler Circuit Time Limit:3000MS     Memory Limit:0KB     64bit IO Format:%lld & %llu Description   Little Joey invented a scrabble machine that he called Euler, after the great mathematician. In his primary school Joey heard about the nice…

That Nice Euler Circuit Time Limit: 3000MS   Memory Limit: 65536K Total Submissions: 1975   Accepted: 624 Description Little Joey invented a scrabble machine that he called Euler, after the great mathematician. In his primary school Joey heard about…

题链: http://poj.org/problem?id=2284 题解: 计算几何,平面图的欧拉定理 欧拉定理:设平面图的定点数为v,边数为e,面数为f,则有 v+f-e=2 即 f=e-v+2 所以$N^2$求出所以线段的交点,并去重, 然后再计算出最后共有多少边,(判断点是否在线段上,是的话则e++) 总的复杂度 $O(N^3)$ 代码: #include<cstdio> #include<cstring> #include<iostream> #include…