- 判断输入的点能不能组成凸包（即所有点都要是凸包的顶点）
- 然后就是求最优三角形划分问题，也就是区间dp
- 感觉这种区间dp还是记忆化搜索写起来比较方便
记忆化搜索
#include<bits/stdc++.h>
using namespace std;
const int inf=0x3fffffff;
int top,s[10024];
struct data
{
int x,y;
} p[10024],temp;
int corss(data a,data b,data c)
{
return ((b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y));
}
double dis(data a,data b)
{
int t=(a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
return sqrt(1.0*t);
}
int cmp(const void *a,const void *b)
{
int m;
data *p1,*p2;
p1=(data *)a;
p2=(data *)b;
m=corss(p[0],*p1,*p2);
if(m<0) return 1;
else if(m==0&&(dis(p[0],*p1)<dis(p[0],*p2)))
return 1;
else return -1;
}
int pt,dp[1024][1024],c[1024][1024];
int cost(int i,int j)
{
int t1=p[i].x+p[j].x;
int t2=p[i].y+p[j].y;
if(t1<0) t1=-t1;
if(t2<0) t2=-t2;
return t1*t2%pt;
}
int get(int s,int t)
{
if(dp[s][t]!=inf) return dp[s][t];
int ans=inf;
for(int k=s+1;k<t;k++)
ans=min(ans,get(s,k)+get(k,t)+c[s][k]+c[k][t]);
return dp[s][t]=ans;
}
int main()
{
int n,i,j,k,u,r;
while(~scanf("%d%d",&n,&pt))
{
for(i=0; i<n; i++) scanf("%d%d",&p[i].x,&p[i].y);
u=0;
for(i=0; i<n; i++)
{
if(p[i].y<p[u].y||((p[i].y==p[u].y)&&p[i].x<p[u].x))
u=i;
}
temp=p[u];
p[u]=p[0];
p[0]=temp;
qsort(&p[1],n-1,sizeof(int)*2,cmp);
for(i=0; i<=2; i++) s[i]=i;
top=2;
for(i=3; i<n; i++)
{
while(corss(p[s[top-1]],p[s[top]],p[i])<=0) top--;
s[++top]=i;
}
if(top!=n-1)
{
printf("I can't cut.\n");
continue;
}
memset(dp,0,sizeof(dp));
for(i=0; i<n; i++)
{
for(j=i; j<n; j++)
dp[i][j]=inf;
dp[i][(i+1)%n]=0;
}
memset(c,0,sizeof(c));
for(i=0; i<n; i++)
for(j=i+2; j<n; j++)
c[j][i]=c[i][j]=cost(s[i],s[j]);
printf("%d\n",get(0,n-1));
}
return 0;
}
直接上
#include<bits/stdc++.h>
using namespace std;
const int inf=0x3f3f3f3f;
int top,s[10024];
struct data
{
int x,y;
} p[10024],temp;
int corss(data a,data b,data c)
{
return ((b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y));
}
double dis(data a,data b)
{
int t=(a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
return sqrt(1.0*t);
}
int cmp(const void *a,const void *b)
{
double m;
data *p1,*p2;
p1=(data *)a;
p2=(data *)b;
m=corss(p[0],*p1,*p2);
if(m<0) return 1;
else if(m==0&&(dis(p[0],*p1)<dis(p[0],*p2)))
return 1;
else return -1;
}
int pt,dp[1024][1024],c[1024][1024];
int cost(int i,int j)
{
int t1=p[i].x+p[j].x;
int t2=p[i].y+p[j].y;
if(t1<0) t1=-t1;
if(t2<0) t2=-t2;
return t1*t2%pt;
}
int main()
{
int n,i,j,k,u,r;
while(~scanf("%d%d",&n,&pt))
{
for(i=0; i<n; i++) scanf("%d%d",&p[i].x,&p[i].y);
u=0;
for(i=0; i<n; i++)
{
if(p[i].y<p[u].y||((p[i].y==p[u].y)&&p[i].x<p[u].x))
u=i;
}
temp=p[u];
p[u]=p[0];
p[0]=temp;
qsort(&p[1],n-1,sizeof(int)*2,cmp);
for(i=0; i<=2; i++) s[i]=i;
top=2;
for(i=3; i<n; i++)
{
while(corss(p[s[top-1]],p[s[top]],p[i])<=0) top--;
s[++top]=i;
}
if(top!=n-1)
{
printf("I can't cut.\n");
continue;
}
memset(dp,0,sizeof(dp));
for(i=0; i<n; i++)
{
for(j=0; j<n; j++)
dp[i][j]=inf;
dp[i][(i+1)%n]=0;
}
memset(c,0,sizeof(c));
for(i=0; i<n; i++)
for(j=i+2; j<n; j++)
c[j][i]=c[i][j]=cost(s[i],s[j]);
for(r=2;r<=n;r++)
{
for(i=0;i<=n-r;i++)
{
j=i+r-1;
for(k=i+1;k<=j-1;k++)
dp[i][j]=min(dp[i][j],dp[i][k]+dp[k][j]+c[i][k]+c[k][j]);
}
}
printf("%d\n",dp[0][n-1]);
}
return 0;
}
直接上
#include<bits/stdc++.h>
using namespace std;
const int inf=0x3f3f3f3f;
int top,s[10024];
struct data
{
int x,y;
} p[10024],temp;
int corss(data a,data b,data c)
{
return ((b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y));
}
double dis(data a,data b)
{
int t=(a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
return sqrt(1.0*t);
}
int cmp(const void *a,const void *b)
{
double m;
data *p1,*p2;
p1=(data *)a;
p2=(data *)b;
m=corss(p[0],*p1,*p2);
if(m<0) return 1;
else if(m==0&&(dis(p[0],*p1)<dis(p[0],*p2)))
return 1;
else return -1;
}
int pt,dp[1024][1024],c[1024][1024];
int cost(int i,int j)
{
int t1=p[i].x+p[j].x;
int t2=p[i].y+p[j].y;
if(t1<0) t1=-t1;
if(t2<0) t2=-t2;
return t1*t2%pt;
}
int main()
{
int n,i,j,k,u,r;
while(~scanf("%d%d",&n,&pt))
{
for(i=0; i<n; i++) scanf("%d%d",&p[i].x,&p[i].y);
u=0;
for(i=0; i<n; i++)
{
if(p[i].y<p[u].y||((p[i].y==p[u].y)&&p[i].x<p[u].x))
u=i;
}
temp=p[u];
p[u]=p[0];
p[0]=temp;
qsort(&p[1],n-1,sizeof(int)*2,cmp);
for(i=0; i<=2; i++) s[i]=i;
top=2;
for(i=3; i<n; i++)
{
while(corss(p[s[top-1]],p[s[top]],p[i])<=0) top--;
s[++top]=i;
}
if(top!=n-1)
{
printf("I can't cut.\n");
continue;
}
memset(dp,0,sizeof(dp));
for(i=0; i<n; i++)
{
for(j=0; j<n; j++)
dp[i][j]=inf;
dp[i][(i+1)%n]=0;
}
memset(c,0,sizeof(c));
for(i=0; i<n; i++)
for(j=i+2; j<n; j++)
c[j][i]=c[i][j]=cost(s[i],s[j]);
for(i=n-3;i>=0;i--)
for(j=i+2;j<n;j++)
for(k=i+1;k<=j-1;k++)
dp[i][j]=min(dp[i][j],dp[i][k]+dp[k][j]+c[i][k]+c[k][j]);
printf("%d\n",dp[0][n-1]);
}
return 0;
}
