SPOJ 375 树链剖分学习

学习树链剖分的第一题，第二个dfs忘记递归了（太蠢），re了两发，改过来以后就1A了。

学习树链剖分可以参考这篇博客：http://blog.sina.com.cn/s/blog_7a1746820100wp67.html 个人感觉写得非常好！！！

树链剖分听起来很吊，其实就是把数边扔到线段树上，然后搞出一点事情来。主要就是一个重儿子，重链，从而使复杂度降到了(logn)。这个非常关键。关于初始化建树：先剖分，求出size,son,w,top,fa,dep数组，就能把树链扔到线段树树上实现了，这个过程也就是两个dfs实现。然后就是简单的区间修改的问题了。（再次感觉那篇博客写得太好了）

树的边权的问题可以转化为树链剖分的问题！！！

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <cmath>
#include <map>
#define LL long long
#define FOR(i,x,y)  for(int i = x;i < y;i ++)
#define IFOR(i,x,y) for(int i = x;i > y;i --)
#define lrt rt<<1
#define rrt rt<<1|1
#define lson rt<<1,l,mid
#define rson rt<<1|1,mid+1,r
#define MAXN 11000

using namespace std;

int n,val[MAXN];

int head[MAXN<<1],edge_cnt;
map <int,int> mat;

struct Edge{
    int u,v,idd,value;
    int nt;
}edge[MAXN<<1];

void add_edge(int u,int v,int idd){
    edge[edge_cnt].u = u;
    edge[edge_cnt].v = v;
    edge[edge_cnt].idd = idd;
    edge[edge_cnt].nt = head[u];
    head[u] = edge_cnt++;
}

int sz[MAXN],son[MAXN],fa[MAXN],dep[MAXN],top[MAXN],id[MAXN],w[MAXN],val0[MAXN],totw;

void dfs1(int u,int father,int depth){
    sz[u] = 1;  dep[u] = depth;  fa[u] = father;
    int idd = -1,maxx = -1;
    for(int i = head[u];i != -1;i = edge[i].nt){
        int v = edge[i].v;
        if(v == father)  continue;
        id[v] = edge[i].idd;
        dfs1(v,u,depth+1);
        sz[u] += sz[v];
        if(sz[v] > maxx)    {idd = v;maxx = sz[v];}
    }
    son[u] = idd;
}

void dfs2(int u,int father){
    if(son[u] == -1)    return;
    top[son[u]] = top[u];
    w[son[u]] = ++totw;
    val[totw] = val0[id[son[u]]];
    mat[id[son[u]]] = totw;
    dfs2(son[u],u);
    for(int i = head[u];i != -1;i = edge[i].nt){
        int v = edge[i].v;
        if(v == father) continue;
        if(v == son[u]) continue;
        top[v] = v;
        w[v] = ++totw;
        val[totw] = val0[id[v]];
        mat[id[v]] = totw;
        dfs2(v,u);
    }
}

struct Tree{
    int l,r;
    int maxx;
}tree[MAXN<<2];

void PushUp(int rt){
    tree[rt].maxx = max(tree[lrt].maxx,tree[rrt].maxx);
}

void Build(int rt,int l,int r){
    tree[rt].l = l; tree[rt].r = r;
    if(l == r){
        tree[rt].maxx = val[l];
        return;
    }
    int mid = (l+r)>>1;
    Build(lson);
    Build(rson);
    PushUp(rt);
}

void Modify(int rt,int x,int value){
    if(tree[rt].l == tree[rt].r){
        tree[rt].maxx = value;
        return;
    }
    int mid = (tree[rt].l + tree[rt].r)>>1;
    if(x <= mid)    Modify(lrt,x,value);
    else Modify(rrt,x,value);
    PushUp(rt);
}

int Query(int rt,int l,int r){
    if(tree[rt].l == l && tree[rt].r == r){
        return tree[rt].maxx;
    }
    int mid = (tree[rt].l + tree[rt].r)>>1;
    if(r <= mid)    return Query(lrt,l,r);
    else if(l > mid)    return Query(rrt,l,r);
    else return max(Query(lson),Query(rson));
}

int solve(int l,int r){
    int ans = -1;
    while(top[l] != top[r]){
        if(dep[top[l]] >= dep[top[r]]){
            ans = max(ans,Query(1,w[top[l]],w[l]));
            l = fa[top[l]];
        }
        else{
            ans = max(ans,Query(1,w[top[r]],w[r]));
            r = fa[top[r]];
        }
    }
    if(l == r)  return ans;
    if(dep[l] >= dep[r]){return max(ans,Query(1,w[r]+1,w[l]));}
    else return max(ans,Query(1,w[l]+1,w[r]));
}

int main(){
    //freopen("test.in","r",stdin);
    int T;
    scanf("%d",&T);
    while(T--){
        scanf("%d",&n);
        int u,v,value;
        memset(head,-1,sizeof(head));
        edge_cnt = 0;
        FOR(i,1,n){
            scanf("%d%d%d",&u,&v,&value);
            add_edge(u,v,i);
            add_edge(v,u,i);
            val0[i] = value;
        }
        dfs1(1,-1,1);
        totw = 0;
        top[1] = 1;
        dfs2(1,-1);
        Build(1,1,totw);
        char op[10];
        while(~scanf("%s",op) && strcmp(op,"DONE")){
            if(strcmp(op,"QUERY") == 0){
                int l,r;
                scanf("%d%d",&l,&r);
                printf("%d\n",solve(l,r));
            }
            else{
                int x,value;
                scanf("%d%d",&x,&value);
                Modify(1,mat[x],value);
            }
        }
    }
    return 0;
}

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