题意 给出正多边形上三个点的坐标,求正多边形的最小面积 分析 先用三边长求出外接圆半径(海伦公式),再求出三边长对应的角度,再求出三个角度的gcd,最后答案即为\(S*2π/gcd\),S为gcd对应的三角形的面积 注意如果三个点在同一段半圆弧上,需要thec=2*pi-thea-theb,而不能直接用acos()函数求 数据卡精度,gcd要取0.001才行,其他不行 #include <bits/stdc++.h> using namespace std; #define ll long l…

C. Ancient Berland Circus time limit per test 2 seconds memory limit per test 64 megabytes input standard input output standard output Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different.…

传送门 题意 给出一正多边形三顶点的坐标,求此正多边形的面积最小值. 分析 为了叙述方便,定义正多边形的单位圆心角u为正多边形的某条边对其外接圆的圆心角(即外接圆的某条弦所对的圆心角). (1)多边形的边数未知,但其外接圆是确定的.多边形的外接圆即三个顶点所构成三角形的外接圆.面积最小即边数最少,单位圆心角最大. (2)设三角形某两边所对的圆心角为a1, a2 (expressed in radians),则最大单位圆心角为 u= gcd(a1, a2, 2PI-a1-a2). 思路 (1)三点…

1C - Ancient Berland Circus 思路: 求出三角形外接圆: 然后找出三角形三条边在小数意义下的最大公约数; 然后n=pi*2/fgcd; 求出面积即可: 代码: #include <cmath> #include <cstdio> #include <cstring> #include <iostream> #include <algorithm> using namespace std; #define INF (1e9…

C. Ancient Berland Circus 题目连接: http://www.codeforces.com/contest/1/problem/C Description Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different. In Ancient Berland arenas in circuses were s…

Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different. In Ancient Berland arenas in circuses were shaped as a regular (equiangular) polygon, the size and the number of angles could vary fro…

题目链接:https://codeforces.com/problemset/problem/1/C 题意:对于一个正多边形,只给出了其中三点的坐标,求这个多边形可能的最小面积,给出的三个点一定能够组成三角形. 思路:根据三角形三个顶点的坐标求得三角形的三边长a.b.c,海伦公式和正弦定理连理得半径R = abc / (4S),再求出外接圆圆心到三角形三个顶点组成的三个圆心角∠1.∠2.∠3的最大公约数作为正多边形的每一份三角形的内角,将所有三角形加起来即可.思路不难但是满满的细节orz,比如防…

CF第一场比赛的最后一题居然是计算几何. 这道题的考点也是比较多,所以来写一篇题解. 前置芝士 平面直角坐标系中两点距离公式:\(l=\sqrt{(X_1-X_2)^2+(Y_1-Y_2)^2}\) 海伦公式:在知道三边时用于计算三角形面积\(S=\sqrt{p(p-a)(p-b)(p-c)}\)(其中\(a,b,c\)为三角形三边,\(p=\frac{a+b+c}{2}\)) 外接圆半径公式:\(R=\frac{abc}{4S}\) 解三角形 (知道三边求角度): \(\cos B=\frac…

C. Ancient Berland Circus time limit per test 2 seconds memory limit per test 64 megabytes input standard input output standard output Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different.…

B. Ancient Berland Hieroglyphs 题目连接: http://codeforces.com/problemset/problem/164/B Descriptionww.co Polycarpus enjoys studying Berland hieroglyphs. Once Polycarp got hold of two ancient Berland pictures, on each of which was drawn a circle of hierog…