树分治入门：例题poj1741
题目链接：Tree
树分治参考资料：09年漆子超 ZigZagK的博客 【点分治】的学习笔记和众多例题
以上的资料是我看过好的，具体算法分析实现都讲明白.
1 //#include<bits/stdc++.h> 2 #include<set> 3 #include<cstdio> 4 #include<iomanip> 5 #include<iostream> 6 #include<string> 7 #include<cstring> 8 #include<algorithm> 9 #define pb push_back 10 #define ll long long 11 #define fi first 12 #define se second 13 #define PI 3.14159265 14 #define ls l,m,rt<<1 15 #define rs m+1,r,rt<<1|1 16 #define eps 1e-7 17 #define pii pair<int,int> 18 typedef unsigned long long ull; 19 const int mod=1e3+5; 20 const ll inf=0x3f3f3f3f3f3f3f; 21 const int maxn=1e5+5; 22 using namespace std; 23 int n,m,head[maxn],to[maxn*2],w[maxn*2],nxt[maxn*2],cnt,k,siz[maxn],dep[maxn],rt,mx[maxn],s; 24 int now[maxn]; 25 bool vis[maxn]; 26 ll ans; 27 void add_edge(int x,int y,int l) 28 { 29 to[++cnt]=y;w[cnt]=l;nxt[cnt]=head[x];head[x]=cnt; 30 } 31 void dfs_rt(int v,int f)//找重心 32 { 33 siz[v]=1;mx[v]=0; 34 //cout<<v<<"SSS"<<f<<endl; 35 for(int i=head[v];i;i=nxt[i]) 36 { 37 if(to[i]==f||vis[to[i]])continue; 38 dfs_rt(to[i],v); 39 siz[v]+=siz[to[i]]; 40 mx[v]=max(siz[to[i]],mx[v]); 41 } 42 mx[v]=max(s-siz[v],mx[v]); 43 if(rt==-1||mx[v]<mx[rt])rt=v; 44 } 45 void get_dep(int v,int f) 46 { 47 now[++now[0]]=dep[v]; 48 for(int i=head[v];i;i=nxt[i]) 49 { 50 if(vis[to[i]]||to[i]==f)continue; 51 dep[to[i]]=dep[v]+w[i]; 52 get_dep(to[i],v); 53 } 54 } 55 int get_sum(int v,int dis) 56 { 57 int cn=0;now[0]=0; 58 dep[v]=dis;get_dep(v,-1); 59 sort(now+1,now+1+now[0]); 60 int l=1,r=now[0]; 61 while(l<r)if(now[l]+now[r]<=k)cn+=r-l,l++;else r--; 62 return cn; 63 } 64 void get_ans(int v) 65 { 66 vis[v]=true;ans+=get_sum(v,0); 67 for(int i=head[v];i;i=nxt[i]) 68 { 69 if(vis[to[i]])continue; 70 ans-=get_sum(to[i],w[i]); 71 rt=-1;s=siz[to[i]];dfs_rt(to[i],v); 72 get_ans(rt); 73 } 74 } 75 int main() 76 { 77 while(~scanf("%d %d",&n,&k)) 78 { 79 if(!n&&!k)break; 80 memset(head,0,sizeof(head));cnt=0;ans=0; 81 memset(vis,0,sizeof(vis)); 82 for(int i=0;i<n-1;i++) 83 { 84 int u,v,l; 85 scanf("%d %d %d",&u,&v,&l); 86 add_edge(u,v,l);add_edge(v,u,l); 87 } 88 rt=-1;s=n;dfs_rt(1,-1); 89 get_ans(rt); 90 printf("%lld\n",ans); 91 } 92 return 0; 93 }
第二个例题：2152: 聪聪可可
题解：跟上面那题差不多，计算出的到根的距离%3之后的值的个数，now[0],now[1],now[2].答案就是now[0]*now[0]+2*now[1]*now[2]
1 #include<bits/stdc++.h> 2 #include<set> 3 #include<cstdio> 4 #include<iomanip> 5 #include<iostream> 6 #include<string> 7 #include<cstring> 8 #include<algorithm> 9 #define pb push_back 10 #define ll long long 11 #define fi first 12 #define se second 13 #define PI 3.14159265 14 #define ls l,m,rt<<1 15 #define rs m+1,r,rt<<1|1 16 #define eps 1e-7 17 #define pii pair<int,int> 18 typedef unsigned long long ull; 19 const int mod=1e3+5; 20 const ll inf=0x3f3f3f3f3f3f3f; 21 const int maxn=2e4+5; 22 using namespace std; 23 int n,m,head[maxn],to[maxn*2],w[maxn*2],nxt[maxn*2],cnt,k,siz[maxn],dep[maxn],rt,mx[maxn],s; 24 int now[maxn]; 25 bool vis[maxn]; 26 int ans; 27 void add_edge(int x,int y,int l) 28 { 29 to[++cnt]=y;w[cnt]=l;nxt[cnt]=head[x];head[x]=cnt; 30 } 31 void dfs_rt(int v,int f)//找重心 32 { 33 siz[v]=1;mx[v]=0; 34 for(int i=head[v];i;i=nxt[i]) 35 { 36 if(to[i]==f||vis[to[i]])continue; 37 dfs_rt(to[i],v); 38 siz[v]+=siz[to[i]]; 39 mx[v]=max(siz[to[i]],mx[v]); 40 } 41 mx[v]=max(s-siz[v],mx[v]); 42 if(rt==-1||mx[v]<mx[rt])rt=v; 43 } 44 void get_dep(int v,int f) 45 { 46 now[(dep[v])%3]++; 47 for(int i=head[v];i;i=nxt[i]) 48 { 49 if(vis[to[i]]||to[i]==f)continue; 50 dep[to[i]]=dep[v]+w[i]; 51 get_dep(to[i],v); 52 } 53 } 54 int get_sum(int v,int dis) 55 { 56 int cn=0;now[0]=0,now[1]=0,now[2]=0; 57 dep[v]=dis;get_dep(v,-1); 58 cn+=now[0]*now[0]+2*now[1]*now[2]; 59 return cn; 60 } 61 void get_ans(int v) 62 { 63 vis[v]=true;ans+=get_sum(v,0); 64 for(int i=head[v];i;i=nxt[i]) 65 { 66 if(vis[to[i]])continue; 67 ans-=get_sum(to[i],w[i]); 68 rt=-1;s=siz[to[i]];dfs_rt(to[i],v); 69 get_ans(rt); 70 } 71 } 72 int main() 73 { 74 while(~scanf("%d",&n)) 75 { 76 memset(head,0,sizeof(head));cnt=0; 77 memset(vis,0,sizeof(vis)); 78 for(int i=0;i<n-1;i++) 79 { 80 int u,v,l; 81 scanf("%d %d %d",&u,&v,&l); 82 add_edge(u,v,l);add_edge(v,u,l); 83 } 84 rt=-1;s=n;dfs_rt(1,-1); 85 get_ans(rt); 86 int sum=n*n; 87 int tmp=__gcd(sum,ans); 88 89 ans/=tmp;sum/=tmp; 90 printf("%d/%d\n",ans,sum); 91 } 92 return 0; 93 }
第三个题： 1316: 树上的询问
在一次树分治的过程中统计到重心的距离，对于每一个q[i]枚举一个点然后二分去找q[i]-dep[i]的个数用lower_bound 和upper_bound相减就可以来。10sec.我9988ms卡过，，，，运气不好就t了
1 #include<bits/stdc++.h> 2 #include<set> 3 #include<cstdio> 4 #include<iomanip> 5 #include<iostream> 6 #include<string> 7 #include<cstring> 8 #include<algorithm> 9 #define pb push_back 10 #define ll long long 11 #define fi first 12 #define se second 13 #define PI 3.14159265 14 #define ls l,m,rt<<1 15 #define rs m+1,r,rt<<1|1 16 #define eps 1e-7 17 #define pii pair<int,int> 18 typedef unsigned long long ull; 19 const int mod=1e3+5; 20 const ll inf=0x3f3f3f3f3f3f3f; 21 const int maxn=2e4+5; 22 using namespace std; 23 int n,m,head[maxn],to[maxn*2],w[maxn*2],nxt[maxn*2],cnt,siz[maxn],dep[maxn],rt,mx[maxn],s,q; 24 int now[maxn],ans[120],que[120]; 25 bool vis[maxn]; 26 void add_edge(int x,int y,int l) 27 { 28 to[++cnt]=y;w[cnt]=l;nxt[cnt]=head[x];head[x]=cnt; 29 } 30 void dfs_rt(int v,int f)//找重心 31 { 32 siz[v]=1;mx[v]=0; 33 for(int i=head[v];i;i=nxt[i]) 34 { 35 if(to[i]==f||vis[to[i]])continue; 36 dfs_rt(to[i],v); 37 siz[v]+=siz[to[i]]; 38 mx[v]=max(siz[to[i]],mx[v]); 39 } 40 mx[v]=max(s-siz[v],mx[v]); 41 if(rt==-1||mx[v]<mx[rt])rt=v; 42 } 43 void get_dep(int v,int f) 44 { 45 now[++now[0]]=dep[v]; 46 for(int i=head[v];i;i=nxt[i]) 47 { 48 if(vis[to[i]]||to[i]==f)continue; 49 dep[to[i]]=dep[v]+w[i]; 50 get_dep(to[i],v); 51 } 52 } 53 int get_sum(int v,int dis,int k) 54 { 55 int cn=0;now[0]=0; 56 dep[v]=dis;get_dep(v,-1); 57 sort(now+1,now+1+now[0]); 58 for(int i=1;i<=now[0];i++) 59 { 60 if(now[i]*2>k)break; 61 cn+=upper_bound(now+1,now+1+now[0],k-now[i])-lower_bound(now+1,now+1+now[0],k-now[i]); 62 } 63 return cn; 64 } 65 void get_ans(int v) 66 { 67 vis[v]=true; 68 for(int i=1;i<=q;i++)ans[i]+=get_sum(v,0,que[i]); 69 for(int i=head[v];i;i=nxt[i]) 70 { 71 if(vis[to[i]])continue; 72 for(int j=1;j<=q;j++)ans[j]-=get_sum(to[i],w[i],que[j]); 73 rt=-1;s=siz[to[i]];dfs_rt(to[i],v); 74 get_ans(rt); 75 } 76 } 77 int main() 78 { 79 scanf("%d %d",&n,&q); 80 for(int i=0;i<n-1;i++) 81 { 82 int u,v,l; 83 scanf("%d %d %d",&u,&v,&l); 84 add_edge(u,v,l);add_edge(v,u,l); 85 } 86 for(int i=1;i<=q;i++) 87 { 88 scanf("%d",&que[i]); 89 } 90 rt=-1;s=n;dfs_rt(1,-1); 91 get_ans(rt); 92 for(int i=1;i<=q;i++) 93 { 94 if(ans[i]) 95 { 96 printf("Yes\n"); 97 } 98 else printf("No\n"); 99 } 100 return 0; 101 }
