[BZOJ1036][ZJOI2008]树的统计Count（树链剖分）

题目描述

传送门

题解

树链剖分模板题。

代码

// BZOJ 1036#include<iostream>#include<cstring>#include<cstdio>using namespace std;const int max_n=3e4+5;const int max_e=max_n*4;const int max_N=max_n*4+5;const int mininf=-2100000000;int n,x,y,N,q,u,t,ans,f1,f2;//w[i]表示点i的权值,size[i]表示以i为根的子树的结点个数,h[i]表示点i的深度,father[i]表示点i的父亲,son[i]表示点i的重儿子 int w[max_n],size[max_n],h[max_n],father[max_n],son[max_n];//top[i]表示点i所在的链的最头上的点,num[i]表示点i在线段树数组中对应的编号,tree[i]表示在线段树数组中编号为i的点在树中对应的点的编号 int top[max_n],num[max_n],tree[max_n];int point[max_n],next[max_e],v[max_e],tot;char order[10];int sum[max_N],maxn[max_N];inline void add(int x,int y){    ++tot; next[tot]=point[x]; point[x]=tot; v[tot]=y;    ++tot; next[tot]=point[y]; point[y]=tot; v[tot]=x;}inline void dfs_1(int x,int fa,int dep){    size[x]=1; h[x]=dep; father[x]=fa;    int maxson=0;    for (int i=point[x];i;i=next[i])      if (v[i]!=fa){        dfs_1(v[i],x,dep+1);        size[x]+=size[v[i]];        if (size[v[i]]>maxson){            maxson=size[v[i]];            son[x]=v[i];          }      }}inline void dfs_2(int x,int fa){    if (son[fa]!=x) top[x]=x;    else top[x]=top[fa];    num[x]=++N;    if (son[x]) dfs_2(son[x],x);    for (int i=point[x];i;i=next[i])      if (v[i]!=fa&&v[i]!=son[x])        dfs_2(v[i],x);}inline void update_sum(int now){    sum[now]=sum[now<<1]+sum[now<<1|1];}inline void update_max(int now){    maxn[now]=max(maxn[now<<1],maxn[now<<1|1]);}inline void build_sum(int now,int l,int r){    int mid=(l+r)>>1;    if (l==r){        sum[now]=w[tree[l]];        return;    }    build_sum(now<<1,l,mid);    build_sum(now<<1|1,mid+1,r);    update_sum(now);}inline void build_max(int now,int l,int r){    int mid=(l+r)>>1;    if (l==r){        maxn[now]=w[tree[l]];        return;    }    build_max(now<<1,l,mid);    build_max(now<<1|1,mid+1,r);    update_max(now);}inline void point_change_sum(int now,int l,int r,int x,int v){    int mid=(l+r)>>1;    if (l==r){        sum[now]=v;        return;    }    if (x<=mid)      point_change_sum(now<<1,l,mid,x,v);    else       point_change_sum(now<<1|1,mid+1,r,x,v);    update_sum(now);}inline void point_change_max(int now,int l,int r,int x,int v){    int mid=(l+r)>>1;    if (l==r){        maxn[now]=v;        return;    }    if (x<=mid)      point_change_max(now<<1,l,mid,x,v);    else      point_change_max(now<<1|1,mid+1,r,x,v);    update_max(now);}inline int query_sum(int now,int l,int r,int lrange,int rrange){    int mid=(l+r)>>1,ans=0;    if (lrange<=l&&r<=rrange) return sum[now];    if (lrange<=mid)      ans+=query_sum(now<<1,l,mid,lrange,rrange);    if (mid+1<=rrange)      ans+=query_sum(now<<1|1,mid+1,r,lrange,rrange);    return ans;}inline int query_max(int now,int l,int r,int lrange,int rrange){    int mid=(l+r)>>1,ans=mininf;    if (lrange<=l&&r<=rrange) return maxn[now];    if (lrange<=mid)      ans=max(ans,query_max(now<<1,l,mid,lrange,rrange));    if (mid+1<=rrange)      ans=max(ans,query_max(now<<1|1,mid+1,r,lrange,rrange));    return ans;}int main(){    scanf("%d",&n);    for (int i=1;i<n;++i){        scanf("%d%d",&x,&y);        add(x,y);    }    for (int i=1;i<=n;++i) scanf("%d",&w[i]);    //预处理size,h,father,son的值     dfs_1(1,0,1);    //预处理top,num,tree的值     dfs_2(1,0);    for (int i=1;i<=n;++i)      tree[num[i]]=i;    build_sum(1,1,N);    build_max(1,1,N);    scanf("%d",&q);    for (int i=1;i<=q;++i){        scanf("%s",order);        while (strlen(order)<4) scanf("%s",order);        scanf("%d%d",&u,&t);        if (order[0]=='C'){            point_change_sum(1,1,N,num[u],t);            point_change_max(1,1,N,num[u],t);        }        else{            if (order[1]=='S'){                ans=0;                f1=top[u],f2=top[t];                while (f1!=f2){                    if (h[f1]<h[f2]){                        swap(u,t);                        swap(f1,f2);                    }                    ans+=query_sum(1,1,N,num[f1],num[u]);                    u=father[f1];                    f1=top[u];                 }                               if (num[u]>num[t]) swap(u,t);                ans+=query_sum(1,1,N,num[u],num[t]);                printf("%d\n",ans);            }            else{                ans=mininf;                f1=top[u],f2=top[t];                while (f1!=f2){                    if (h[f1]<h[f2]){                        swap(u,t);                        swap(f1,f2);                    }                    ans=max(ans,query_max(1,1,N,num[f1],num[u]));                    u=father[f1];                    f1=top[u];                }                if (num[u]>num[t]) swap(u,t);                ans=max(ans,query_max(1,1,N,num[u],num[t]));                printf("%d\n",ans);            }        }           }}

手写栈

#include<iostream>#include<cstring>#include<cstdio>using namespace std;const int max_n=3e4+5;const int max_e=max_n*4;const int max_N=max_n*4+5;const int mininf=-2100000000;int n,x,y,N,q,u,t,ans,f1,f2;int w[max_n],size[max_n],h[max_n],father[max_n],son[max_n];int top[max_n],num[max_n],tree[max_n];int strack[max_n],cur[max_n],use[max_n];int point[max_n],nxt[max_e],v[max_e],tot;char order[10];int sum[max_N],maxn[max_N];inline void add(int x,int y){    ++tot; nxt[tot]=point[x]; point[x]=tot; v[tot]=y;    ++tot; nxt[tot]=point[y]; point[y]=tot; v[tot]=x;}inline void dfs_1(){    int temp=0;    strack[++temp]=1; size[1]=1; h[1]=1;    for (int i=1;i<=n;++i) cur[i]=point[i];    while (temp)    {        int x=strack[temp];        if (v[cur[x]]==father[x]) cur[x]=nxt[cur[x]];        if (!cur[x])        {            temp--;            if (father[x])            {                size[father[x]]+=size[x];                if (size[x]>size[son[father[x]]]) son[father[x]]=x;            }            continue;        }        int vt=v[cur[x]];        strack[++temp]=vt;        size[vt]=1; h[vt]=h[x]+1; father[vt]=x;        cur[x]=nxt[cur[x]];    }}inline void dfs_2(){    int temp=0;    strack[++temp]=1; num[1]=++N; top[1]=1;    for (int i=1;i<=n;++i) cur[i]=point[i];    while (temp)    {        int x=strack[temp];        if (!use[x])        {            use[x]=1;            int vt=son[x];            if (vt)            {                strack[++temp]=vt;                top[vt]=top[x];                num[vt]=++N;            }            continue;        }        while (cur[x]&&(v[cur[x]]==father[x]||v[cur[x]]==son[x])) cur[x]=nxt[cur[x]];        if (!cur[x])        {            temp--;            continue;        }        else        {            int vt=v[cur[x]];            strack[++temp]=vt;            top[vt]=vt;            num[vt]=++N;            cur[x]=nxt[cur[x]];        }    }}inline void update_sum(int now){    sum[now]=sum[now<<1]+sum[now<<1|1];}inline void update_max(int now){    maxn[now]=max(maxn[now<<1],maxn[now<<1|1]);}inline void build_sum(int now,int l,int r){    int mid=(l+r)>>1;    if (l==r){        sum[now]=w[tree[l]];        return;    }    build_sum(now<<1,l,mid);    build_sum(now<<1|1,mid+1,r);    update_sum(now);}inline void build_max(int now,int l,int r){    int mid=(l+r)>>1;    if (l==r){        maxn[now]=w[tree[l]];        return;    }    build_max(now<<1,l,mid);    build_max(now<<1|1,mid+1,r);    update_max(now);}inline void point_change_sum(int now,int l,int r,int x,int v){    int mid=(l+r)>>1;    if (l==r){        sum[now]=v;        return;    }    if (x<=mid)      point_change_sum(now<<1,l,mid,x,v);    else       point_change_sum(now<<1|1,mid+1,r,x,v);    update_sum(now);}inline void point_change_max(int now,int l,int r,int x,int v){    int mid=(l+r)>>1;    if (l==r){        maxn[now]=v;        return;    }    if (x<=mid)      point_change_max(now<<1,l,mid,x,v);    else      point_change_max(now<<1|1,mid+1,r,x,v);    update_max(now);}inline int query_sum(int now,int l,int r,int lrange,int rrange){    int mid=(l+r)>>1,ans=0;    if (lrange<=l&&r<=rrange) return sum[now];    if (lrange<=mid)      ans+=query_sum(now<<1,l,mid,lrange,rrange);    if (mid+1<=rrange)      ans+=query_sum(now<<1|1,mid+1,r,lrange,rrange);    return ans;}inline int query_max(int now,int l,int r,int lrange,int rrange){    int mid=(l+r)>>1,ans=mininf;    if (lrange<=l&&r<=rrange) return maxn[now];    if (lrange<=mid)      ans=max(ans,query_max(now<<1,l,mid,lrange,rrange));    if (mid+1<=rrange)      ans=max(ans,query_max(now<<1|1,mid+1,r,lrange,rrange));    return ans;}int main(){    scanf("%d",&n);    for (int i=1;i<n;++i){        scanf("%d%d",&x,&y);        add(x,y);    }    for (int i=1;i<=n;++i) scanf("%d",&w[i]);    dfs_1();    dfs_2();    for (int i=1;i<=n;++i)      tree[num[i]]=i;    build_sum(1,1,N);    build_max(1,1,N);    scanf("%d",&q);    for (int i=1;i<=q;++i){        scanf("%s",order);        scanf("%d%d",&u,&t);        if (order[0]=='C'){            point_change_sum(1,1,N,num[u],t);            point_change_max(1,1,N,num[u],t);        }        else{            if (order[1]=='S'){                ans=0;                f1=top[u],f2=top[t];                while (f1!=f2){                    if (h[f1]<h[f2]){                        swap(u,t);                        swap(f1,f2);                    }                    ans+=query_sum(1,1,N,num[f1],num[u]);                    u=father[f1];                    f1=top[u];                 }                               if (num[u]>num[t]) swap(u,t);                ans+=query_sum(1,1,N,num[u],num[t]);                printf("%d\n",ans);            }            else{                ans=mininf;                f1=top[u],f2=top[t];                while (f1!=f2){                    if (h[f1]<h[f2]){                        swap(u,t);                        swap(f1,f2);                    }                    ans=max(ans,query_max(1,1,N,num[f1],num[u]));                    u=father[f1];                    f1=top[u];                }                if (num[u]>num[t]) swap(u,t);                ans=max(ans,query_max(1,1,N,num[u],num[t]));                printf("%d\n",ans);            }        }           }}

总结

①线段树要开4n，不要开2n
②线段树的操作可以合并