POJ 3241 曼哈頓最小產生樹

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感覺講解，寫的非常詳細，http://blog.csdn.net/huzecong/article/details/8576908

重點是一個定理： Hint For the graph on the right, there exists a minimum spanning tree in which there is at most one vertex connected with A in the shadow area. You can extend this property to solve the problem.

 

#include<cstdio>#include<algorithm>#define N 100010#define INF 0x3f3f3f3fusing namespace std;struct point{    int x,y,id;    bool operator<(const point &p) const    { return x==p.x?y<p.y:x<p.x;}}p[N];struct edge{    int a,b,w;    bool operator<(const edge &x) const    { return w<x.w;}}e[N<<2];struct BIT{    int w,p;}bit[N];int n,k,m,tot,ans;int f[N],a[N],b[N];int abs(int x){    return x<0?-x:x;}int find(int x){    return x==f[x]?x:f[x]=find(f[x]);}int query(int x){    int r=INF,p=-1;    while(x<=m)    {        if (bit[x].w<r) r=bit[x].w,p=bit[x].p;        x+=x&-x;    }    return p;}void update(int x, int w, int p){    while(x>0)    {        if (bit[x].w>w) bit[x].w=w,bit[x].p=p;        x-=x&-x;    }}void addedge(int a, int b, int w){    ++tot;    e[tot].a=a,e[tot].b=b,e[tot].w=w;}int dist(point a, point b){    return abs(a.x-b.x)+abs(a.y-b.y);}int main(){    while(scanf("%d%d",&n,&k)!=EOF)    {        tot=0;        for (int i=1;i<=n;i++)        {            scanf("%d%d",&p[i].x,&p[i].y);            p[i].id=i;        }        for (int dir=1;dir<=4;dir++)        {            if (dir==2||dir==4)                for (int i=1;i<=n;i++) swap(p[i].x,p[i].y);            else  if (dir==3)                for (int i=1;i<=n;i++) p[i].x=-p[i].x;            sort(p+1,p+n+1);            for (int i=1;i<=n;i++) a[i]=b[i]=p[i].y-p[i].x;            sort(b+1,b+1+n);            m=unique(b+1,b+1+n)-b-1;            for (int i=1;i<=n;i++) a[i]=lower_bound(b+1,b+m+1,a[i])-b;            for (int i=1;i<=m;i++) bit[i].w=INF,bit[i].p=-1;            for (int i=n;i>=1;i--)            {                int pos=query(a[i]);                if (pos!=-1) addedge(p[i].id,p[pos].id,dist(p[i],p[pos]));                update(a[i],p[i].x+p[i].y,i);            }        }        sort(e+1,e+tot+1);        for (int i=1;i<=n;i++) f[i]=i;        for (int i=1,ec=n;ec>k&&i<=tot;i++)            if (find(e[i].a)!=find(e[i].b))        {            f[find(e[i].a)]=find(e[i].b);            if (--ec==k) ans=e[i].w;        }        printf("%d\n",ans);    }    return 0;}

　　

POJ 3241 曼哈頓最小產生樹