题意:给定 n 个不三点共线的点,然后问你能组成多少锐角或者直角三角形。
析:可以反过来求,求有多少个钝角三角形,然后再用总的减去,直接求肯定会超时,但是可以枚举每个点,以该点为钝角的那个顶点,然后再枚举另一条边,维护与该边大于90度并小于等于180度的点的数量,这里要用极角排序,这样就可以减小时间复杂度,但是会WA,要控制精度,但是精度是个迷,表示不会。
代码如下:
#pragma comment(linker, "/STACK:1024000000,1024000000") #include <cstdio> #include <string> #include <cstdlib> #include <cmath> #include <iostream> #include <cstring> #include <set> #include <queue> #include <algorithm> #include <vector> #include <map> #include <cctype> #include <cmath> #include <stack> #include <sstream> #include <list> #include <assert.h> #include <bitset> #include <numeric> #define debug() puts("++++") #define gcd(a, b) __gcd(a, b) #define lson l,m,rt<<1 #define rson m+1,r,rt<<1|1 #define fi first #define se second #define pb push_back #define sqr(x) ((x)*(x)) #define ms(a,b) memset(a, b, sizeof a) #define sz size() #define be begin() #define ed end() #define pu push_up #define pd push_down #define cl clear() #define lowbit(x) -x&x //#define all 1,n,1 #define FOR(i,n,x) for(int i = (x); i < (n); ++i) #define freopenr freopen("in.in", "r", stdin) #define freopenw freopen("out.out", "w", stdout) using namespace std; typedef long long LL; typedef unsigned long long ULL; typedef pair<int, int> P; const int INF = 0x3f3f3f3f; const LL LNF = 1e17; const double inf = 1e20; const double PI = acos(-1.0); const double eps = 1e-8; const int maxn = 1500 + 50; const int maxm = 1e6 + 10; const LL mod = 1000000000000000LL; const int dr[] = {-1, 1, 0, 0, 1, 1, -1, -1}; const int dc[] = {0, 0, 1, -1, 1, -1, 1, -1}; const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"}; int n, m; const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; inline bool is_in(int r, int c) { return r >= 0 && r < n && c >= 0 && c < m; } inline int readInt(){ int x; scanf("%d", &x); return x; } int a[maxn], b[maxn]; double p[maxn<<1]; int main(){ int kase = 0; while(scanf("%d", &n) == 1 && n){ for(int i = 0; i < n; ++i) scanf("%d %d", a + i, b + i); int ans = 0; for(int i = 0; i < n; ++i){ int cnt = 0; for(int j = 0; j < n; ++j) if(i != j) p[cnt++] = atan2(b[j]-b[i], a[j]-a[i]); sort(p, p + cnt); for(int j = 0; j < cnt; ++j) p[j+cnt] = p[j] + PI * 2.; int k = 0, l = 0; for(int j = 0; j < cnt; ++j){ while(p[k] - p[j] + eps <= PI / 2.) ++k; while(p[l] - p[j] + eps < PI) ++l; ans += l - k; } } ans = n * (n-1) * (n-2) / 6 - ans; if(n < 3) ans = 0; printf("Scenario %d:\n", ++kase); printf("There are %d sites for making valid tracks\n", ans); } return 0; }
原文地址:https://www.cnblogs.com/dwtfukgv/p/8970060.html
时间: 2024-10-17 09:49:12