Cake ZOJ - 3537

http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=3537

学会了求凸包 其实就是单调栈的思想 详见https://blog.csdn.net/codeswarrior/article/details/81327277

然后就是裸的凸多边形三角划分 区间DP即可

#include <bits/stdc++.h>
using namespace std;
const int maxn=3e2+10;

struct node
{
    int x,y;
};

node stk[maxn];
node point[maxn],pre[maxn],suf[maxn];
int dp[maxn][maxn],cost[maxn][maxn];
int n,m,top,n1,n2;

bool cmp(node n1,node n2)
{
    if(n1.x==n2.x) return n1.y>n2.y;
    else return n1.x<n2.x;
}

int cmpk(node p1,node p2,node p3)
{
    return (p2.y-p1.y)*(p3.x-p1.x)>(p3.y-p1.y)*(p2.x-p1.x);
}

bool judge()
{
    node cur1,cur2;
    int i;

    top=0;
    stk[++top]=point[1],stk[++top]=point[2];
    for(i=3;i<=n;i++){
        while(top>=2&&cmpk(stk[top-1],stk[top],point[i])) top--;
        stk[++top]=point[i];
    }
    for(i=1;i<=top;i++) pre[i]=stk[i];
    n1=top;
    //for(i=1;i<=n1;i++) printf("*%d %d*\n",pre[i].x,pre[i].y);

    top=0;
    stk[++top]=point[n],stk[++top]=point[n-1];
    for(i=n-2;i>=1;i--){
        while(top>=2&&cmpk(stk[top-1],stk[top],point[i])) top--;
        stk[++top]=point[i];
    }
    for(i=1;i<=top;i++) suf[i]=stk[i];
    n2=top;
    //for(i=1;i<=n2;i++) printf("*%d %d*\n",suf[i].x,suf[i].y);

    if(n1+n2-2<n) return 0;
    else{
        n=0;
        for(i=1;i<=n1;i++){
            point[++n]=pre[i];
        }
        for(i=2;i<=n2-1;i++){
            point[++n]=suf[i];
        }
        return 1;
    }
}

int getval(node p1,node p2)
{
    return abs(p1.x+p2.x)*abs(p1.y+p2.y)%m;
}

int main()
{
    int i,j,k,l;
    while(scanf("%d%d",&n,&m)!=EOF){
        for(i=1;i<=n;i++){
            scanf("%d%d",&point[i].x,&point[i].y);
        }
        sort(point+1,point+n+1,cmp);
        if(judge()){
            //for(i=1;i<=n;i++) printf("*%d %d*\n",point[i].x,point[i].y);
            memset(dp,0x3f,sizeof(dp));
            for(i=1;i+1<=n;i++) dp[i][i+1]=0;
            memset(cost,0,sizeof(cost));
            for(i=1;i<=n;i++){
                for(j=i+2;j<=n;j++){
                    cost[i][j]=getval(point[i],point[j]);
                }
            }
            for(l=3;l<=n;l++){
                for(i=1;i+l-1<=n;i++){
                    j=i+l-1;
                    //printf("***%d %d***\n",i,j);
                    for(k=i+1;k<=j-1;k++){
                        dp[i][j]=min(dp[i][j],dp[i][k]+dp[k][j]+cost[i][k]+cost[k][j]);
                    }
                }
            }
            printf("%d\n",dp[1][n]);
        }
        else printf("I can't cut.\n");
    }
    return 0;
}

/*
4 100000
1 2
3 1
4 2
2 3
*/