zoj3537 Cake 【凸包+最优三角形划分】

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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;}/*测试数据：3 30 01 10 24 1000 01 00 11 14 1000 03 00 31 1OutPut:01I can't cut.*/

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;}

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