【HDU】5574 Colorful Tree【子树染色，询问子树颜色数——线段树+bit+lca+set】

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题目链接：【HDU】5574 Colorful Tree

题目大意：对一个子树染色，询问一个子树的颜色数。
题目分析：set维护每种颜色所在的dfs序区间，修改均摊nlogn。

#include <bits/stdc++.h>using namespace std ;typedef long long LL ;typedef pair < int , int > pii ;#define clr( a , x ) memset ( a , x , sizeof a )const int MAXN = 100005 ;const int MAXE = 200005 ;struct Edge {    int v , n ;    Edge () {}    Edge ( int v , int n ) : v ( v ) , n ( n ) {}} ;Edge E[MAXE] ;int H[MAXN] , cntE ;int dep[MAXN] ;int pre[MAXN] ;int top[MAXN] ;int son[MAXN] ;int siz[MAXN] ;int tree_idx ;int in[MAXN] ;int ou[MAXN] ;int dfs_idx ;int n , q ;set < pii > s , col[MAXN] ;set < pii > :: iterator it , it1 ;int c[MAXN] ;int T[MAXN] ;int setv[MAXN << 2] ;void addedge ( int u , int v ) {    E[cntE] = Edge ( v , H[u] ) ;    H[u] = cntE ++ ;}void dfs ( int u ) {    in[u] = ++ dfs_idx ;    siz[u] = 1 ;    son[u] = 0 ;    for ( int i = H[u] ; ~i ; i = E[i].n ) {        int v = E[i].v ;        if ( v == pre[u] ) continue ;        pre[v] = u ;        dep[v] = dep[u] + 1 ;        dfs ( v ) ;        siz[u] += siz[v] ;        if ( siz[son[u]] < siz[v] ) son[u] = v ;    }    ou[u] = dfs_idx ;}void rebuild ( int u , int top_element ) {    top[u] = top_element ;    if ( son[u] ) rebuild ( son[u] , top_element ) ;    for ( int i = H[u] ; ~i ; i = E[i].n ) {        int v = E[i].v ;        if ( v != pre[u] && v != son[u] ) rebuild ( v , v ) ;    }}int lca ( int x , int y ) {    while ( top[x] != top[y] ) dep[top[x]] > dep[top[y]] ? x = pre[top[x]] : y = pre[top[y]] ;    return dep[x] < dep[y] ? x : y ;}void build ( int o , int l , int r ) {    setv[o] = 0 ;    if ( l == r ) {        setv[o] = c[in[l]] ;        return ;    }    int m = l + r >> 1 ;    build ( o << 1 , l , m ) ;    build ( o << 1 | 1 , m + 1 , r ) ;}void down ( int o ) {    if ( setv[o] ) {        setv[o << 1] = setv[o << 1 | 1] = setv[o] ;        setv[o] = 0 ;    }}void update ( int L , int R , int v , int o , int l , int r ) {    if ( L <= l && r <= R ) {        setv[o] = v ;        return ;    }    down ( o ) ;    int m = l + r >> 1 ;    if ( L <= m ) update ( L , R , v , o << 1 , l , m ) ;    if ( m <  R ) update ( L , R , v , o << 1 | 1 , m + 1 , r ) ;}int query ( int x , int o , int l , int r ) {    while ( l < r ) {        down ( o ) ;        int m = l + r >> 1 ;        if ( x <= m ) o = o << 1 , r = m ;        else o = o << 1 | 1 , l = m + 1 ;    }    return setv[o] ;}void add ( int x , int v ) {    for ( int i = x ; i <= n ; i += i & -i ) T[i] += v ;}int sum ( int x , int ans = 0 ) {    for ( int i = x ; i >= 1 ; i -= i & -i ) ans += T[i] ;    return ans ;}int get ( int x ) {    int x1 = 0 , x2 = 0 ;    if ( it != col[c[x]].begin () ) {        it1 = it ;        -- it1 ;        x1 = lca ( it1->second , x ) ;    }    it1 = it ;    ++ it1 ;    if ( it1 != col[c[x]].end () ) x2 = lca ( it1->second , x ) ;    if ( dep[x1] > dep[x2] ) return x1 ;    return x2 ;}void solve () {    int op , x , y ;    scanf ( "%d" , &n ) ;    cntE = dfs_idx = tree_idx = 0 ;    s.clear () ;    for ( int i = 1 ; i <= n ; ++ i ) {        H[i] = -1 ;        col[i].clear () ;        T[i] = 0 ;    }    for ( int i = 1 ; i < n ; ++ i ) {        scanf ( "%d%d" , &x , &y ) ;        addedge ( x , y ) ;        addedge ( y , x ) ;    }    dep[1] = 1 ;    dfs ( 1 ) ;    rebuild ( 1 , 1 ) ;    for ( int i = 1 ; i <= n ; ++ i ) {        scanf ( "%d" , &c[i] ) ;        col[c[i]].insert ( make_pair ( in[i] , i ) ) ;        s.insert ( make_pair ( in[i] , i ) ) ;    }    build ( 1 , 1 , n ) ;    for ( int i = 1 ; i <= n ; ++ i ) {        int pre = 0 ;        for ( it = col[i].begin () ; it != col[i].end () ; ++ it ) {            add ( it->first , 1 ) ;            if ( pre ) add ( in[lca ( pre , it->second )] , -1 ) ;            pre = it->second ;        }    }    scanf ( "%d" , &q ) ;    for ( int i = 1 ; i <= q ; ++ i ) {        scanf ( "%d%d" , &op , &x ) ;        pii tmp ( in[x] , x ) ;        if ( op == 0 ) {            scanf ( "%d" , &y ) ;            while ( 1 ) {                it = s.lower_bound ( tmp ) ;                if ( it == s.end () || it->first > ou[x] ) break ;                int u = it->second ;                it = col[c[u]].find ( *it ) ;                int x1 = get ( u ) ;                if ( x1 ) add ( in[x1] , 1 ) ;                add ( in[u] , -1 ) ;                pii tmp1 = *it ;                s.erase ( tmp1 ) ;                col[c[u]].erase ( tmp1 ) ;                c[u] = y ;            }            c[x] = y ;            s.insert ( tmp ) ;            col[y].insert ( tmp ) ;            it = col[y].find ( tmp ) ;            int x1 = get ( x ) ;            if ( x1 ) add ( in[x1] , -1 ) ;            add ( in[x] , 1 ) ;            update ( in[x] , ou[x] , y , 1 , 1 , n ) ;        } else {            int ans = sum ( ou[x] ) - sum ( in[x] - 1 ) ;            it = s.lower_bound ( tmp ) ;            if ( it == s.end () ) ++ ans ;            else if ( it->second != x ) {                int color = query ( in[x] , 1 , 1 , n ) ;                it = col[color].lower_bound ( tmp ) ;                if ( it == col[color].end () || it->first > ou[x] ) ++ ans ;            }            printf ( "%d\n" , ans ) ;        }    }}int main () {    int T ;    scanf ( "%d" , &T ) ;    for ( int i = 1 ; i <= T ; ++ i ) {        printf ( "Case #%d:\n" , i ) ;        solve () ;    }    return 0 ;}

压缩后代码：

#include <bits/stdc++.h>using namespace std;typedef long long LL;typedef pair<int ,int >pii;#define clr(a,x) memset(a,x,sizeof a)const int MAXN=100005;const int MAXE=200005;struct Edge{    int v,n;    Edge(){}    Edge(int v,int n):v(v),n(n){}}E[MAXE];int H[MAXN],cntE;int dep[MAXN],pre[MAXN],top[MAXN],son[MAXN],siz[MAXN],tree_idx;int in[MAXN],ou[MAXN],dfs_idx;set<pii>s,col[MAXN];set<pii>::iterator it,it1;int c[MAXN],T[MAXN],setv[MAXN<<2],n,q;void addedge(int u,int v){E[cntE]=Edge(v,H[u]);H[u]=cntE++;}void dfs(int u){    in[u]=++dfs_idx;    siz[u]=1;    son[u]=0;    for(int i=H[u];~i;i=E[i].n){        int v=E[i].v;        if(v==pre[u])continue;        pre[v]=u;        dep[v]=dep[u]+1;        dfs(v);        siz[u]+=siz[v];        if(siz[son[u]]<siz[v])son[u]=v;    }    ou[u]=dfs_idx;}void rebuild(int u,int top_element){    top[u]=top_element;    if(son[u])rebuild(son[u],top_element);    for(int i=H[u];~i;i=E[i].n)if(E[i].v!=pre[u]&&E[i].v!=son[u])rebuild(E[i].v,E[i].v);}int lca(int x,int y){    while(top[x]!=top[y])dep[top[x]]>dep[top[y]]?x=pre[top[x]]:y=pre[top[y]];    return dep[x]<dep[y]?x:y;}void build(int o,int l,int r){    setv[o]=0;    if(l==r)setv[o]=c[in[l]];    else {        int m=l+r>>1;        build(o<<1,l,m);        build(o<<1|1,m+1,r);    }}void down(int o){if(setv[o])setv[o<<1]=setv[o<<1|1]=setv[o],setv[o]=0;}void update(int L,int R,int v,int o,int l,int r){    if(L<=l&&r<=R)setv[o]=v;    else {        down(o);        int m=l+r>>1;        if(L<=m)update(L,R,v,o<<1,l,m);        if(m<R)update(L,R,v,o<<1|1,m+1,r);    }}int query(int x,int o,int l,int r){    for(int m=l+r>>1;l<r;x<=m?(o=o<<1,r=m):(o=o<<1|1,l=m+1),m=l+r>>1)down(o);    return setv[o];}void add(int x,int v){for(int i=x;i<=n;i+=i&-i)T[i]+=v;}int sum(int x,int ans=0){    for(int i=x;i>=1;i-=i&-i)ans+=T[i];    return ans;}int get(int x,int x1=0,int x2=0){    if(it!=col[c[x]].begin())x1=lca((--(it1=it))->second,x);    if((++(it1=it))!=col[c[x]].end())x2=lca(it1->second,x);    if(dep[x1]>dep[x2])return x1;    return x2;}void solve(){    int op,x,y;    scanf("%d",&n);    cntE=dfs_idx=tree_idx=0;    s.clear();    for(int i=1;i<=n;++i)H[i]=-1,col[i].clear(),T[i]=0;    for(int i=1;i<n;addedge(x,y),addedge(y,x),++i)scanf("%d%d",&x,&y);    dfs(dep[1]=1),rebuild(1,1);    for(int i=1;i<=n;++i){        scanf("%d",&c[i]);        col[c[i]].insert(make_pair(in[i],i));        s.insert(make_pair(in[i],i));    }    build(1,1,n);    for(int i=1,pre=0;i<=n;++i,pre=0){        for(it=col[i].begin();it!=col[i].end();++it){            add(it->first,1);            if(pre)add(in[lca(pre,it->second)],-1);            pre=it->second;        }    }    scanf("%d",&q);    for(int i=1;i<=q;++i){        scanf("%d%d",&op,&x);        pii tmp(in[x],x);        if(op==0){            scanf("%d",&y);            while(1){                it=s.lower_bound(tmp);                if(it==s.end()||it->first>ou[x])break;                int u=it->second;                it=col[c[u]].find(*it);                int x1=get(u);                if(x1)add(in[x1],1);                add(in[u],-1);                pii tmp1=*it;                s.erase(tmp1);                col[c[u]].erase(tmp1);                c[u]=y;            }            c[x]=y;            s.insert(tmp);            col[y].insert(tmp);            it=col[y].find(tmp);            int x1=get(x);            if(x1)add(in[x1],-1);            add(in[x],1);            update(in[x],ou[x],y,1,1,n);        }else{            int ans=sum(ou[x])-sum(in[x]-1);            it=s.lower_bound(tmp);            if(it==s.end())++ans;            else if(it->second!=x){                int color=query(in[x],1,1,n);                it=col[color].lower_bound(tmp);                if(it==col[color].end()||it->first>ou[x])++ans;            }            printf("%d\n",ans);        }    }}int main(){    int T;    scanf("%d",&T);    for(int i=1;i<=T;++i){        printf("Case #%d:\n",i);        solve();    }    return 0;}

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