COJ 0500 杨老师的路径规划（MST）最小生成树

动态的最小生成树LCT：

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cmath>
 4 #include<algorithm>
 5 #include<queue>
 6 #include<cstring>
 7 #define PAU putchar(‘ ‘)
 8 #define ENT putchar(‘\n‘)
 9 #define CH for(int d=0;d<=1;d++) if(ch[d])
10 using namespace std;
11 const int maxn=100+10,maxm=5000+10,inf=-1u>>1;
12 struct node{
13     node*fa,*ch[2],*mx;int x;bool rev;
14     node(){fa=ch[0]=ch[1]=NULL;mx=this;x=0;rev=false;}
15     void revt(){swap(ch[0],ch[1]);rev^=1;return;}
16     void update(){mx=this;CH{if(mx->x<ch[d]->mx->x)mx=ch[d]->mx;}return;}
17     void down(){if(rev){CH{ch[d]->revt();}rev=false;}return;}
18 }lct[maxn+maxm],*nodecnt;
19 int parent(node*x,node*&y){return (y=x->fa)?y->ch[0]==x?0:y->ch[1]==x?1:-1:-1;}
20 void rotate(node*x){
21     node*y,*z;int d1=parent(x,y),d2=parent(y,z);
22     if(y->ch[d1]=x->ch[d1^1]) y->ch[d1]->fa=y;
23     y->fa=x;x->fa=z;x->ch[d1^1]=y;
24     if(d2!=-1) z->ch[d2]=x;
25     y->update();return;
26 }
27 void pushdown(node*x){
28     static node*s[maxn];int top=0;
29     for(node*y;;x=y){
30         s[top++]=x;y=x->fa;
31         if(!y||(y->ch[0]!=x&&y->ch[1]!=x)) break;
32     } while(top--) s[top]->down();return;
33 }
34 node*splay(node*x){
35     pushdown(x);node*y,*z;int d1,d2;
36     while(true){
37         if((d1=parent(x,y))<0) break;
38         if((d2=parent(y,z))<0){rotate(x);break;}
39         if(d1==d2) rotate(y),rotate(x);
40         else rotate(x),rotate(x);
41     } x->update();return x;
42 }
43 node*access(node*x){
44     node*ret=NULL;
45     for(;x;x=x->fa) splay(x)->ch[1]=ret,(ret=x)->update();
46     return ret;
47 }
48 void makeroot(int x){access(x+lct)->revt();return;}
49 void link(int x,int y){makeroot(x);splay(x+lct)->fa=lct+y;return;}
50 void cut(int x,int y){
51     makeroot(x);node*p=(access(y+lct),splay(y+lct));
52     p->ch[0]=p->ch[0]->fa=NULL;p->update();return;
53 }
54 node*findtop(int x){
55     node*t=(access(x+lct),splay(x+lct));while(t->ch[0]) t->down(),t=t->ch[0];return t;
56 }
57 node*query(int x,int y){
58     makeroot(x);return access(y+lct)->mx;
59 }
60 int n,m;
61 inline int read(){
62     int x=0,sig=1;char ch=getchar();
63     while(!isdigit(ch)){if(ch==‘-‘)sig=-1;ch=getchar();}
64     while(isdigit(ch))x=10*x+ch-‘0‘,ch=getchar();
65     return x*=sig;
66 }
67 inline void write(int x){
68     if(x==0){putchar(‘0‘);return;}if(x<0)putchar(‘-‘),x=-x;
69     int len=0,buf[15];while(x)buf[len++]=x%10,x/=10;
70     for(int i=len-1;i>=0;i--)putchar(buf[i]+‘0‘);return;
71 }
72 int s[maxm],t[maxm];
73 void init(){
74     n=read();m=n*(n-1)>>1;int ans=0;nodecnt=lct+n+1;
75     for(int i=1;i<=m;i++){
76         s[i]=read();t[i]=read();node*q=nodecnt++;q->x=read();int k=q-lct;makeroot(k);
77         if(findtop(s[i])!=findtop(t[i])){
78             link(s[i],k);link(t[i],k);ans+=q->x;
79         }else{
80             node*p=query(s[i],t[i]);if(p->x<q->x) continue;
81             ans+=q->x-p->x;int id=p-lct-n;
82             cut(s[id],p-lct);cut(t[id],p-lct);
83             link(s[i],k);link(t[i],k);
84         }
85     } write(ans);
86     return;
87 }
88 void work(){
89     return;
90 }
91 void print(){
92     return;
93 }
94 int main(){init();work();print();return 0;}

静态Kruskal：

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cmath>
 4 #include<algorithm>
 5 #include<queue>
 6 #include<cstring>
 7 #define PAU putchar(‘ ‘)
 8 #define ENT putchar(‘\n‘)
 9 using namespace std;
10 const int maxn=100+10,maxm=5000+10;
11 struct edge{int x,y,w;}e[maxm];
12 bool cmp(edge a,edge b){return a.w<b.w;}
13 inline int read(){
14     int x=0,sig=1;char ch=getchar();
15     while(!isdigit(ch)){if(ch==‘-‘)sig=-1;ch=getchar();}
16     while(isdigit(ch))x=10*x+ch-‘0‘,ch=getchar();
17     return x*=sig;
18 }
19 inline void write(int x){
20     if(x==0){putchar(‘0‘);return;}if(x<0)putchar(‘-‘),x=-x;
21     int len=0,buf[15];while(x)buf[len++]=x%10,x/=10;
22     for(int i=len-1;i>=0;i--)putchar(buf[i]+‘0‘);return;
23 }
24 int n,m,fa[maxn];
25 int findset(int x){return (fa[x]==x)?x:fa[x]=findset(fa[x]);}
26 void init(){
27     n=read();m=n*(n-1)>>1;
28     for(int i=1;i<=n;i++) fa[i]=i;
29     int x,y;
30     for(int i=1;i<=m;i++){
31         x=read();y=read();
32         e[i]=(edge){x,y,read()};
33     }
34     sort(e+1,e+1+m,cmp);
35     int ans=0,cnt=0;
36     for(int i=1;i<=m;i++){
37         int x=findset(e[i].x),y=findset(e[i].y);
38         if(x!=y){
39             fa[y]=x;ans+=e[i].w;
40             if(++cnt==n-1) break;
41         }
42     } write(ans);
43     return;
44 }
45 void work(){
46     return;
47 }
48 void print(){
49     return;
50 }
51 int main(){init();work();print();return 0;}