【刷題】BZOJ 1132 [POI2008]Tro
阿新 • • 發佈:2018-12-08
Description
平面上有N個點. 求出所有以這N個點為頂點的三角形的面積和 N<=3000
Input
第一行給出數字N,N在[3,3000] 下面N行給出N個點的座標,其值在[0,10000]
Output
保留一位小數,誤差不超過0.1
Sample Input
5
0 0
1 2
0 2
1 0
1 1
Sample Output
7.0
Solution
\(ans=\frac{1}{2}\sum_{i=1}^n\sum_{j=i+1}^n\sum_{k=j+1}^n|(y_j-y_i)(x_k-x_i)-(y_k-y_i)(x_j-x_i)|\)
列舉第一個點,求出其它點的相對座標
然後為了去絕對值,讓所有點按計較排序,保證叉積是正的
\(ans_i=\frac{1}{2}\sum_{j=i+1}^n\sum_{k=j+1}^ny_j*x_k-y_k*x_j\)
\(~~~~~~~~~=\frac{1}{2}(\sum_{j=i+1}^ny_j\sum_{k=j+1}^nx_k-\sum_{j=i+1}^nx_j\sum_{k=j+1}^ny_k)\)
對最後的 \(\sum\) 做字首和就好了
#include<bits/stdc++.h> #define ui unsigned int #define ll long long #define db double #define ld long double #define ull unsigned long long #define REP(a,b,c) for(register int a=(b),a##end=(c);a<=a##end;++a) #define DEP(a,b,c) for(register int a=(b),a##end=(c);a>=a##end;--a) const int MAXN=3000+10; int n,cnt; ld ans; struct point{ int x,y; inline bool operator < (const point &A) const { return y<A.y; }; }; point pt[MAXN]; struct cross{ int x,y; ld k; inline bool operator < (const cross &A) const { return k>A.k; }; }; cross cs[MAXN]; template<typename T> inline void read(T &x) { T data=0,w=1; char ch=0; while(ch!='-'&&(ch<'0'||ch>'9'))ch=getchar(); if(ch=='-')w=-1,ch=getchar(); while(ch>='0'&&ch<='9')data=((T)data<<3)+((T)data<<1)+(ch^'0'),ch=getchar(); x=data*w; } template<typename T> inline void write(T x,char ch='\0') { if(x<0)putchar('-'),x=-x; if(x>9)write(x/10); putchar(x%10+'0'); if(ch!='\0')putchar(ch); } template<typename T> inline void chkmin(T &x,T y){x=(y<x?y:x);} template<typename T> inline void chkmax(T &x,T y){x=(y>x?y:x);} template<typename T> inline T min(T x,T y){return x<y?x:y;} template<typename T> inline T max(T x,T y){return x>y?x:y;} int main() { read(n); REP(i,1,n)read(pt[i].x),read(pt[i].y); std::sort(pt+1,pt+n+1); REP(i,3,n) { REP(j,1,i-1)cs[j]=(cross){pt[i].x-pt[j].x,pt[i].y-pt[j].y,atan2((ld)(pt[i].x-pt[j].x),(ld)(pt[i].y-pt[j].y))}; std::sort(cs+1,cs+i);ld sx=0,sy=0; REP(j,1,i-1) { if(j!=1)ans+=sx*(ld)cs[j].y-(ld)cs[j].x*sy; sx+=(ld)cs[j].x,sy+=(ld)cs[j].y; } } printf("%.1Lf\n",ans/2); return 0; }