BZOJ：2243: [SDOI2011]染色

题解：

树剖，线段树维护区间颜色段数

记录两端点的颜色，做到O(1)合并

问题：

　　非递归建树实现

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn=;

int n,m;
int incolor[maxn];

int cntedge;
int head[maxn];
int to[maxn<<],nex[maxn<<];
int addedge(int x,int y){
    nex[++cntedge]=head[x];
    to[cntedge]=y;
    head[x]=cntedge;
}

int father[maxn],depth[maxn],siz[maxn];
int heavyson[maxn],top[maxn],idx[maxn],ref[maxn];

int dfs1(int now,int fa){
    father[now]=fa;
    depth[now]=depth[fa]+;
    siz[now]=;
    for(int i=head[now];i;i=nex[i]){
        if(to[i]==fa)continue;
        dfs1(to[i],now);
        siz[now]+=siz[to[i]];
        if(siz[to[i]]>siz[heavyson[now]]){
            heavyson[now]=to[i];
        }
    }
}
int temp;
int dfs2(int now,int toppoint){
    top[now]=toppoint;
    idx[now]=(++temp);
    ref[temp]=now;
    if(!heavyson[now])return ;
    dfs2(heavyson[now],toppoint);
    for(int i=head[now];i;i=nex[i]){
        if(to[i]==father[now])continue;
        if(to[i]==heavyson[now])continue;
        dfs2(to[i],to[i]);
    }
}

struct SegmentTree{
    int l,r;
    int lcolor,rcolor;
    int setcolor,sum;
}tree[maxn<<];
int pushup(int now){
    tree[now].lcolor=tree[now<<].lcolor;
    tree[now].rcolor=tree[now<<|].rcolor;
    if(tree[now<<].rcolor==tree[now<<|].lcolor){
        tree[now].sum=tree[now<<].sum+tree[now<<|].sum-;
    }else{
        tree[now].sum=tree[now<<].sum+tree[now<<|].sum;
    }
}
int pushdown(int now){
    if(tree[now].setcolor!=-){
        tree[now<<].setcolor=tree[now<<].lcolor=tree[now<<].rcolor=tree[now].setcolor;
        tree[now<<|].setcolor=tree[now<<|].lcolor=tree[now<<|].rcolor=tree[now].setcolor;
        tree[now<<].sum=tree[now<<|].sum=;
        tree[now].setcolor=-;
    }
}

int Build(int now,int l,int r){
    tree[now].l=l;tree[now].r=r;
    tree[now].setcolor=-;
    if(l==r){
        tree[now].lcolor=tree[now].rcolor=incolor[ref[l]];
        tree[now].sum=;
        return ;
    }
    int mid=(l+r)>>;
    Build(now<<,l,mid);
    Build(now<<|,mid+,r);
    pushup(now);
}

int Updata(int now,int ll,int rr,int x){
    if(tree[now].l>=ll&&tree[now].r<=rr){
        tree[now].setcolor=tree[now].lcolor=tree[now].rcolor=x;
        tree[now].sum=;
        return ;
    }
    int mid=(tree[now].l+tree[now].r)>>;
    pushdown(now);
    if(ll<=mid)Updata(now<<,ll,rr,x);
    if(rr>mid)Updata(now<<|,ll,rr,x);
    pushup(now);
}

int Querysum(int now,int ll,int rr){
    if(tree[now].l>=ll&&tree[now].r<=rr){
        return tree[now].sum;
    }
    int mid=(tree[now].l+tree[now].r)>>;
    pushdown(now);
    if(rr<=mid)return Querysum(now<<,ll,rr);
    else if(ll>mid)return Querysum(now<<|,ll,rr);
    else if(tree[now<<].rcolor==tree[now<<|].lcolor)return Querysum(now<<,ll,rr)+Querysum(now<<|,ll,rr)-;
    else return Querysum(now<<,ll,rr)+Querysum(now<<|,ll,rr);
}

int Querycolor(int now,int p){
    if(tree[now].l==tree[now].r){
        return tree[now].lcolor;
    }
    int mid=(tree[now].l+tree[now].r)>>;
    pushdown(now);
    if(p<=mid)return Querycolor(now<<,p);
    else return Querycolor(now<<|,p);
}

int Change(int u,int v,int x){
    int tu=top[u];
    int tv=top[v];
    while(tu!=tv){
        if(depth[tu]<depth[tv]){
            swap(tu,tv);swap(u,v);
        }
        Updata(,idx[tu],idx[u],x);
        u=father[tu];tu=top[u];
    }
    if(depth[u]>depth[v])swap(u,v);
    Updata(,idx[u],idx[v],x);
}

int Getans(int u,int v){
    int ret=;
    int tu=top[u];
    int tv=top[v];
    while(tu!=tv){
        if(depth[tu]<depth[tv]){
            swap(tu,tv);swap(u,v);
        }
        ret=ret+Querysum(,idx[tu],idx[u]);
        u=father[tu];
        if(Querycolor(,idx[u])==Querycolor(,idx[tu]))--ret;
        tu=top[u];
    }
    if(depth[u]>depth[v])swap(u,v);
    ret=ret+Querysum(,idx[u],idx[v]);
    return ret;
}

int minit(){
    temp=cntedge=;
    memset(heavyson,,sizeof(heavyson));
    memset(head,,sizeof(head));
}

int main(){
    scanf("%d%d",&n,&m);
    minit();

    for(int i=;i<=n;++i)scanf("%d",&incolor[i]);
    for(int i=;i<=n-;++i){
        int x,y;
        scanf("%d%d",&x,&y);
        addedge(x,y);addedge(y,x);
    }
    dfs1(,);
    dfs2(,);
    Build(,,n);

    char opty[];
    while(m--){
        int x,y,z;
        scanf("%s",opty);
        if(opty[]=='C'){
            scanf("%d%d%d",&x,&y,&z);
            Change(x,y,z);
        }else{
            scanf("%d%d",&x,&y);
            printf("%d\n",Getans(x,y));
        }
    }
    return ;
}