题意:给出一些点表示多边形顶点的位置(如果多边形是凹多边形就不能切),切多边形时每次只能在顶点和顶点间切,每切一次都有相应的代价。现在已经给出计算代价的公式,问把多边形切成最多个不相交三角形的最小代价是多少。
#include<bits/stdc++.h> #define ll long long #define INF 0x3f3f3f3f using namespace std; const double eps = 1e-10; double dcmp(double x) { if(fabs(x) < eps) return 0; else return x < 0 ? -1 : 1; } struct Point { double x, y; Point(double x=0, double y=0):x(x),y(y) {} }; vector<Point> v; Point operator - ( const Point &A ,const Point &B) { return Point(A.x-B.x, A.y-B.y); } bool operator == (const Point& p1, const Point& p2) { return p1.x == p2.x && p1.y == p2.y; } bool operator < (const Point& p1, const Point& p2) { return p1.x < p2.x || (p1.x == p2.x && p1.y < p2.y); } double Cross(const Point& A, const Point& B) { return A.x*B.y - A.y*B.x; } double Dot(const Point& A, const Point& B) { return A.x*B.x + A.y*B.y; } int cross(Point p0,Point p1,Point p2) //计算叉积 p0p1 X p0p2 { return (p1.x-p0.x)*(p2.y-p0.y)-(p1.y-p0.y)*(p2.x-p0.x); } double dis(Point p1,Point p2) //计算 p1p2的 距离 { return sqrt((double)(p2.x-p1.x)*(p2.x-p1.x)+(p2.y-p1.y)*(p2.y-p1.y)); } bool cmp(Point p1,Point p2) //极角排序函数 , 角度相同则距离小的在前面 { int tmp=cross(v[0],p1,p2); if(tmp>0) return true; else if(tmp==0&&dis(v[0],p1)<dis(v[0],p2)) return true; else return false; } vector<Point> ConvexHull(vector<Point> p) { // 预处理,删除重复点 sort(p.begin(), p.end()); p.erase(unique(p.begin(), p.end()), p.end()); int n = p.size(); int m = 0; vector<Point> ch(n+1); for(int i = 0; i < n; i++) { while(m > 1 && Cross(ch[m-1]-ch[m-2], p[i]-ch[m-2]) <= 0) m--; ch[m++] = p[i]; } int k = m; for(int i = n-2; i >= 0; i--) { while(m > k && Cross(ch[m-1]-ch[m-2], p[i]-ch[m-2]) <= 0) m--; ch[m++] = p[i]; } if(n > 1) m--; ch.resize(m); return ch; } int f[305][305]; int dp[305][305]; vector<Point> s; int main(){ int n,m; int xx,yy; while(scanf("%d%d",&n,&m)>0){ for(int i=0;i<n;i++){ scanf("%d%d",&xx,&yy); v.push_back({xx,yy}); } s = ConvexHull(v); if(s.size()!=n ){ cout << "I can't cut.\n"; v.clear(); continue; } else{ sizeof(f,0,sizeof(f)); for (int i=0; i<n; i++) { for (int j=i+2; j<n; j++) f[i][j] = f[j][i] = ( ((ll)fabs(s[i].x + s[j].x) ) * ((ll)fabs(s[i].y + s[j].y) ))%m; } for (int i=0; i<n; i++) { for (int j=0; j<n; j++) dp[i][j] = INF; dp[i][(i+1)%n]=0; } for (int i=n-3; i>=0; i--)//区间dp求解 { for (int j=i+2; j<n; j++) { for (int k=i+1; k<j; k++) { dp[i][j]=min(dp[i][j], dp[i][k]+dp[k][j]+f[i][k]+f[k][j]); } } } cout<<dp[0][n-1]<<endl; } v.clear(); s.clear(); } } /* 4 100 1 1 2 1 1 2 2 2 */