hdu 4946 Area of Mushroom 计算几何

这题卡了我几天，主要是因为求凸包的时候用叉乘排序不能有重点，有重点的时候必须先删掉重点，然后才能用叉乘排序。

于是我用了atan2()先求出角度，然后再排序的。

atan2排序版本：

#include <stdio.h>#include <math.h>#include <stdlib.h>#include <string.h>#include <iostream>#include <algorithm>#define eps 1e-8#define pi acos(-1.0)using namespace std;struct Node {    int x,y,v,mark,r,flag;    double degree;};Node a[505];int n,fx,fy;bool cmp1(Node a1,Node a2){    if(a1.v==a2.v){        if(a1.y == a2.y)            return a1.x < a2.x;        else             return a1.y < a2.y;    }    return a2.v<a1.v;}bool cmpconvex(Node a1,Node a2){    if(fabs(a1.degree-a2.degree)<eps){            if(a1.x==a2.x&&a1.y==a2.y)                return a1.mark < a2.mark;            else if(a1.y == a2.y)                return a1.x < a2.x;            else                 return a1.y < a2.y;    }    return a1.degree < a2.degree;}bool cmp3(Node a1,Node a2){    return a1.r < a2.r;}void Debug(){    for(int i=0;i<n;i++){        printf("%d %d %d\n",a[i].v,a[i].r,a[i].flag);    }    puts("");}void Debugp(int t,Node * p){    for(int i=0;i<t;i++){        printf("%d %d\n",p[i].x,p[i].y);    }    puts("");}void DebugD(int t,Node * p){    for(int i=0;i<t;i++){        printf("%d %d %d %lf\n",p[i].x,p[i].y,p[i].mark,p[i].degree);    }    puts("");}int cross(Node a1,Node a2,Node a3){    return (a2.x-a1.x)*(a3.y-a2.y)-(a3.x-a2.x)*(a2.y-a1.y);}int ConvexHull(Node * p,Node * ans,int t){    for(int i=1;i<t;i++){        if(p[i].y==p[0].y){            if(p[i].x<p[0].x)swap(p[i],p[0]);        }        else if(p[i].y<p[0].y){            swap(p[i],p[0]);        }    }    ans[0] = p[0];    if(t==1)return 1;    sort(p,p+t,cmpconvex);    //Debugp(t,p);    //DebugD(t,p);    ans[1] = p[1];    int k=1,j=2;    while(j<t){        if(p[j].mark>1){j++;continue;}        while(cross(ans[k-1],ans[k],p[j])<0){            if(k<2)break;            k--;        }        ans[k+1] = p[j];        j++;k++;    }    //Debugp(k+1,ans);    return k+1;}void solve(){    sort(a,a+n,cmp1);    //Debug();    int t = n;    for(int i=1;i<n;i++){        if(a[i].v!=a[0].v){            t = i;            break;        }    }    Node p[505];    Node ans[505];    for(int i=1;i<t;i++){        if(a[i-1].x==a[i].x&&a[i-1].y==a[i].y){            if(i-1==0){                a[i-1].mark = 1;                a[i]  .mark = 2;            }            else if(a[i-2].mark > 0){                if(a[i-1].x==a[i-2].x&&a[i-1].y==a[i-2].y){                    a[i-1].mark = a[i-2].mark + 1;                    a[i].mark   = a[i-1].mark + 1;                }                else {                    a[i-1].mark = 1;                    a[i].mark = 2;                }            }            else {                a[i-1].mark = 1;                a[i].mark = 2;            }        }    }    for(int i=0;i<t;i++){        p[i] = a[i];    }    int lenc = ConvexHull(p,ans,t);    for(int i=0;i<t;i++){        for(int j=1;j<=lenc;j++){            if(cross(ans[j-1],ans[j%lenc],p[i])==0){                if(!p[i].mark&&p[i].v){                    p[i].flag = 1;                    //printf("%d %d %d\n",i,a[i].x,a[i].y);                    break;                                    }            }        }    }    sort(a,a+n,cmp3);    //Debug();    for(int i=0;i<t;i++){        a[p[i].r].flag = p[i].flag;    }    //Debug();    for(int i=0;i<n;i++){    printf("%d",a[i].flag);    }    puts("");}void input(){    int t = 1;    while(scanf("%d",&n),n){        printf("Case #%d: ",t++);        memset(a,0,sizeof(a));        for(int i=0;i<n;i++){            scanf("%d %d %d",&a[i].x,&a[i].y,&a[i].v);            a[i].r = i;        }        solve();    }}void File(){    freopen("4946.in","r",stdin);    freopen("a.out","w",stdout);}int main(void){    //File();    input();    return 0;}

删重点，叉乘版本：

#include <stdio.h>#include <math.h>#include <stdlib.h>#include <string.h>#include <iostream>#include <algorithm>#define eps 1e-8#define pi acos(-1.0)using namespace std;struct Node {    int x,y,v,mark,r,flag;    double degree;};Node a[505];int n,fx,fy;bool cmp1(Node a1,Node a2){    if(a1.v==a2.v){        if(a1.y == a2.y)            return a1.x < a2.x;        else             return a1.y < a2.y;    }    return a2.v<a1.v;}bool cmpconvex1(Node a1,Node a2){    if((a1.x-fx)*(a2.y-fy)==(a1.y-fy)*(a2.x-fx)){            if(a1.y == a2.y)                return a1.x < a2.x;            else                 return a1.y < a2.y;    }    return (a1.x-fx)*(a2.y-fy)>(a1.y-fy)*(a2.x-fx);}bool cmp3(Node a1,Node a2){    return a1.r < a2.r;}void Debug(){    for(int i=0;i<n;i++){        printf("%d %d %d\n",a[i].v,a[i].r,a[i].flag);    }    puts("");}void Debugp(int t,Node * p){    for(int i=0;i<t;i++){        printf("%d %d\n",p[i].x,p[i].y);    }    puts("");}void DebugD(int t,Node * p){    for(int i=0;i<t;i++){        printf("%d %d %d %lf\n",p[i].x,p[i].y,p[i].mark,p[i].degree);    }    puts("");}int cross(Node a1,Node a2,Node a3){    return (a2.x-a1.x)*(a3.y-a2.y)-(a3.x-a2.x)*(a2.y-a1.y);}int ConvexHull(Node * p,Node * ans,int t){    for(int i=1;i<t;i++){        if(p[i].y==p[0].y){            if(p[i].x<p[0].x)swap(p[i],p[0]);        }        else if(p[i].y<p[0].y){            swap(p[i],p[0]);        }    }    ans[0] = p[0];    fx = p[0].x;    fy = p[0].y;    if(t==1)return 1;    sort(p,p+t,cmpconvex1);    //Debugp(t,p);    //DebugD(t,p);    ans[1] = p[1];    int k=1,j=2;    while(j<t){        while(cross(ans[k-1],ans[k],p[j])<0){            if(k<2)break;            k--;        }        ans[k+1] = p[j];        j++;k++;    }    if(ans[1].mark>1){        for(int i = 1;i<k;i++){            ans[i] = ans[i+1];         }        k--;    }    //Debugp(k+1,ans);    return k+1;}void solve(){    sort(a,a+n,cmp1);    //Debug();    int t = n;    for(int i=1;i<n;i++){        if(a[i].v!=a[0].v){            t = i;            break;        }    }    Node p[505];    Node ans[505];    //delete repeat nodes    for(int i=0;i<t-1;i++){        if(a[i].x==a[i+1].x&&a[i].y==a[i+1].y){            a[i].mark = 1;            a[i+1].mark = 1;        }    }    int k = 0;    for(int i=0;i<t-1;i++){        if(a[i].x!=a[i+1].x||a[i].y!=a[i+1].y){            p[k++] = a[i];        }    }    p[k++] = a[t-1];    //for(int i=0;i<t;i++){    //    p[i] = a[i];    //}    int lenc = ConvexHull(p,ans,k);    for(int i=0;i<k;i++){        for(int j=1;j<=lenc;j++){            if(cross(ans[j-1],ans[j%lenc],p[i])==0){                if(!p[i].mark&&p[i].v){                    p[i].flag = 1;                    //printf("%d %d %d\n",i,a[i].x,a[i].y);                    break;                                    }            }        }    }    sort(a,a+n,cmp3);    //Debug();    for(int i=0;i<k;i++){        a[p[i].r].flag = p[i].flag;    }    //Debug();    for(int i=0;i<n;i++){    printf("%d",a[i].flag);    }    puts("");}void input(){    int t = 1;    while(scanf("%d",&n),n){        printf("Case #%d: ",t++);        memset(a,0,sizeof(a));        for(int i=0;i<n;i++){            scanf("%d %d %d",&a[i].x,&a[i].y,&a[i].v);            a[i].r = i;        }        solve();    }}void File(){    freopen("4946.in","r",stdin);    freopen("c.out","w",stdout);}int main(void){    //File();    input();    return 0;}

水平排序删重点版本：

#include <stdio.h>#include <math.h>#include <stdlib.h>#include <string.h>#include <iostream>#include <algorithm>#define eps 1e-8#define pi acos(-1.0)using namespace std;struct Node {    int x,y,v,mark,r,flag;    double degree;};Node a[1010];int n,fx,fy;bool cmp1(Node a1,Node a2){    if(a1.v==a2.v){        if(a1.y == a2.y)            return a1.x < a2.x;        else             return a1.y < a2.y;    }    return a2.v<a1.v;}bool cmpconvex1(Node a1,Node a2){    if((a1.x-fx)*(a2.y-fy)==(a1.y-fy)*(a2.x-fx)){            if(a1.y == a2.y)                return a1.x < a2.x;            else                 return a1.y < a2.y;    }    return (a1.x-fx)*(a2.y-fy)>(a1.y-fy)*(a2.x-fx);}bool cmpconvex2(Node a1,Node a2){            if(a1.y == a2.y)                return a1.x < a2.x;            else                 return a1.y < a2.y;}bool cmp3(Node a1,Node a2){    return a1.r < a2.r;}void Debug(){    for(int i=0;i<n;i++){        printf("%d %d %d\n",a[i].v,a[i].r,a[i].flag);    }    puts("");}void Debugp(int t,Node * p){    for(int i=0;i<t;i++){        printf("%d %d\n",p[i].x,p[i].y);    }    puts("");}void DebugD(int t,Node * p){    for(int i=0;i<t;i++){        printf("%d %d %d %lf\n",p[i].x,p[i].y,p[i].mark,p[i].degree);    }    puts("");}int cross(Node a1,Node a2,Node a3){    return (a2.x-a1.x)*(a3.y-a2.y)-(a3.x-a2.x)*(a2.y-a1.y);}int ConvexHull(Node * p,Node * ans,int t){    sort(p,p+t,cmpconvex2);    //Debugp(t,p);    //DebugD(t,p);    for(int i=0;i<t-1;i++){        p[2*t-2-i] = p[i];    }    int k = 0;    for(int j=0;j<2*t-1;j++){        while(k>=2&&cross(ans[k-2],ans[k-1],p[j])<0){            k--;        }        ans[k++] = p[j];    }    if(t==1)return 1;    //Debugp(k+1,ans);    return k-1;}void solve(){    sort(a,a+n,cmp1);    //Debug();    int t = n;    for(int i=1;i<n;i++){        if(a[i].v!=a[0].v){            t = i;            break;        }    }    Node p[1010];    Node ans[1010];    //delete repeat nodes    for(int i=0;i<t-1;i++){        if(a[i].x==a[i+1].x&&a[i].y==a[i+1].y){            a[i].mark = 1;            a[i+1].mark = 1;        }    }    int k = 0;    for(int i=0;i<t-1;i++){        if(a[i].x!=a[i+1].x||a[i].y!=a[i+1].y){            p[k++] = a[i];        }    }    p[k++] = a[t-1];    //for(int i=0;i<t;i++){    //    p[i] = a[i];    //}    int lenc = ConvexHull(p,ans,k);    for(int i=0;i<k;i++){        for(int j=1;j<=lenc;j++){            if(cross(ans[j-1],ans[j%lenc],p[i])==0){                if(!p[i].mark&&p[i].v){                    p[i].flag = 1;                    //printf("%d %d %d\n",i,a[i].x,a[i].y);                    break;                                    }            }        }    }    sort(a,a+n,cmp3);    //Debug();    for(int i=0;i<k;i++){        a[p[i].r].flag = p[i].flag;    }    //Debug();    for(int i=0;i<n;i++){    printf("%d",a[i].flag);    }    puts("");}void input(){    int t = 1;    while(scanf("%d",&n),n){        printf("Case #%d: ",t++);        memset(a,0,sizeof(a));        for(int i=0;i<n;i++){            scanf("%d %d %d",&a[i].x,&a[i].y,&a[i].v);            a[i].r = i;        }        solve();    }}void File(){    freopen("4946.in","r",stdin);    freopen("c.out","w",stdout);}int main(void){    //File();    input();    return 0;}

水平排序不删重点版：

#include <stdio.h>#include <math.h>#include <stdlib.h>#include <string.h>#include <iostream>#include <algorithm>#define eps 1e-8#define pi acos(-1.0)using namespace std;struct Node {    int x,y,v,mark,r,flag;    double degree;};Node a[1010];int n,fx,fy;bool cmp1(Node a1,Node a2){    if(a1.v==a2.v){        if(a1.y == a2.y)            return a1.x < a2.x;        else             return a1.y < a2.y;    }    return a2.v<a1.v;}bool cmpconvex1(Node a1,Node a2){    if((a1.x-fx)*(a2.y-fy)==(a1.y-fy)*(a2.x-fx)){            if(a1.y == a2.y)                return a1.x < a2.x;            else                 return a1.y < a2.y;    }    return (a1.x-fx)*(a2.y-fy)>(a1.y-fy)*(a2.x-fx);}bool cmp3(Node a1,Node a2){    return a1.r < a2.r;}void Debug(){    for(int i=0;i<n;i++){        printf("%d %d %d\n",a[i].v,a[i].r,a[i].flag);    }    puts("");}void Debugp(int t,Node * p){    for(int i=0;i<t;i++){        printf("%d %d\n",p[i].x,p[i].y);    }    puts("");}void DebugD(int t,Node * p){    for(int i=0;i<t;i++){        printf("%d %d %d %lf\n",p[i].x,p[i].y,p[i].mark,p[i].degree);    }    puts("");}int cross(Node a1,Node a2,Node a3){    return (a2.x-a1.x)*(a3.y-a2.y)-(a3.x-a2.x)*(a2.y-a1.y);}int ConvexHull(Node * p,Node * ans,int t){    //DebugD(t,p);    for(int i=0;i<t-1;i++){        p[2*t-2-i] = p[i];    }    int k = 1;    ans[0] = p[0];    if(t==1)return 1;    for(int j=1;j<2*t-1;j++){        if(p[j].x==p[j-1].x&&p[j].y==p[j-1].y)continue;        while(k>=2&&cross(ans[k-2],ans[k-1],p[j])<0){            k--;        }        ans[k++] = p[j];    }    //Debugp(k+1,ans);    return k-1;}void solve(){    sort(a,a+n,cmp1);    //Debug();    int t = n;    for(int i=1;i<n;i++){        if(a[i].v!=a[0].v){            t = i;            break;        }    }    Node p[1010];    Node ans[1010];    for(int i=0;i<t-1;i++){        if(a[i].x==a[i+1].x&&a[i].y==a[i+1].y){            a[i].mark = 1;            a[i+1].mark = 1;        }    }    for(int i=0;i<t;i++){        p[i] = a[i];    }    int lenc = ConvexHull(p,ans,t);    for(int i=0;i<t;i++){        for(int j=1;j<=lenc;j++){            if(cross(ans[j-1],ans[j%lenc],p[i])==0){                if(!p[i].mark&&p[i].v){                    p[i].flag = 1;                    //printf("%d %d %d\n",i,a[i].x,a[i].y);                    break;                                    }            }        }    }    sort(a,a+n,cmp3);    //Debug();    for(int i=0;i<t;i++){        a[p[i].r].flag = p[i].flag;    }    //Debug();    for(int i=0;i<n;i++){    printf("%d",a[i].flag);    }    puts("");}void input(){    int t = 1;    while(scanf("%d",&n),n){        printf("Case #%d: ",t++);        memset(a,0,sizeof(a));        for(int i=0;i<n;i++){            scanf("%d %d %d",&a[i].x,&a[i].y,&a[i].v);            a[i].r = i;        }        solve();    }}void File(){    freopen("4946.in","r",stdin);    freopen("c.out","w",stdout);}int main(void){    //File();    input();    return 0;}