SPOJ QTREE 375. Query on a tree

树链剖分。。。

375. Query on a tree Problem code: QTREE

You are given a tree (an acyclic undirected connected graph) with N nodes, and edges numbered 1, 2, 3...N-1.

We will ask you to perfrom some instructions of the following form:

• CHANGE i ti : change the cost of the i-th edge to ti
  or
• QUERY a b : ask for the maximum edge cost on the path from node a to node b

Input

The first line of input contains an integer t, the number of test cases (t <= 20). t test cases follow.

For each test case:

• In the first line there is an integer N (N <= 10000),
• In the next N-1 lines, the i-th line describes the i-th edge: a line with three integers a b c denotes an edge between a, b of cost c (c <= 1000000),
• The next lines contain instructions "CHANGE i ti" or "QUERY a b",
• The end of each test case is signified by the string "DONE".

There is one blank line between successive tests.

Output

For each "QUERY" operation, write one integer representing its result.

Example

Input:
1
3
1 2 1
2 3 2
QUERY 1 2
CHANGE 1 3
QUERY 1 2
DONE
Output:
1
3

Source Code

<pre name="code" class="cpp">#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;

const int N = 100100;
#define prt(k) cout<<#k" = "<<k<<endl;
struct Edge
{
    int to, next;
}e[N<<2];
int head[N], Size;
void init_edge()
{
    memset(head, -1, sizeof head);
    Size = 0;
}
void addedge(int u, int v)
{
    e[Size] = (Edge) {v, head[u]};
    head[u] = Size++;
}
int siz[N], dep[N], fa[N], top[N], son[N], p[N];
int n;

void dfs1(int u, int pre, int d)
{
    siz[u] = 1;
    fa[u] = pre;
    dep[u] = d;
    for(int i=head[u];~i;i=e[i].next)
    {
        int v = e[i].to;
        if(v == pre) continue;
        dfs1(v, u, d + 1);
        siz[u] += siz[v];
        if(son[u]==-1 || siz[son[u]] < siz[v])
            son[u] = v;
    }
}
int pos;
void getPOS(int u, int to)
{
    top[u] = to;
    p[u] = pos++;
    if(~son[u]) getPOS(son[u], to);
    for(int i=head[u];~i;i=e[i].next)
    {
        int v = e[i].to;
        if(v-fa[u] && v-son[u])
            getPOS(v, v);
    }
}
void init()
{
    memset(son, -1, sizeof son);
    init_edge();
    pos = 0;
}
/***********Tree*************/
int tree[N<<2];
#define ls o*2
#define rs o*2+1
#define lson l,m,ls
#define rson m+1,r,rs
void build(int l,int r,int o)
{
    tree[o] = 0;
    if(l==r) return ;
    int m = (l+r) /2;
    build(lson);
    build(rson);
}
void pushup(int o)
{
    tree[o] = max(tree[ls], tree[rs]);
}
void update(int pos, int val, int l=1, int r=n, int o=1)
{
    if(l==r)
    {
        if(l==pos) tree[o] = val;
        return;
    }
    int m = (l+r)/2;
    if(pos<=m) update(pos, val, lson);
    else update(pos, val, rson);
    pushup(o);
}
int query(int L, int R, int l,int r, int o)
{
    if(L<=l && r<=R) return tree[o];
    int m = (l+r)/ 2;
    int res=0;
    if(L<=m) res=max(res, query(L,R,lson));
    if(m<R) res=max(res,query(L,R,rson));
    return res;
}
inline int query(int L, int R)
{
   // if(L>R) swap(L, R); if(L<1) L = 1;
    return query(L,R, 1,n,1);
}
/*********End Tree*************/
inline int find(int u, int v)
{
    int f1 = top[u], f2 = top[v], tmp = 0;
    while(f1 - f2)
    {
        if(dep[f1] < dep[f2])
            swap(f1, f2), swap(u,v);
        tmp = max(tmp, query(p[f1], p[u]));
        u = fa[f1]; f1 = top[u];
      //  cout<<u<<endl;
    }
    if(u==v) return tmp;
    if(dep[u] > dep[v]) swap(u, v);
    return max(tmp, query(p[son[u]], p[v]));
}
int g[N][3];
inline void read(int &a)
{
    char c = 0;
    while(!isdigit(c)) c=getchar();
    a = 0;
    while(isdigit(c)) a = a * 10 + c - '0', c = getchar();
}
void show(int l ,int r, int o)
{
    printf("[%d, %d] : tree[%d] = %d\n", l, r, o, tree[o]);
    if(l==r) return;
    int  m = (l+r) / 2;
    show(lson);
    show(rson);
    if(o==1) putchar(10);
}
int main()
{
   // int a,b; read(a); read(b); cout<<a<<' '<<b<<endl;
   // freopen("qtree.in", "r", stdin);
    int T; scanf("%d", &T);
    while(T--)
    {
        scanf("%d", &n); n--;
        init();
        for(int i=1;i<=n;i++) {
            int a,b,c;
            read(a); read(b); read(c);
          //  scanf("%d%d%d", &a, &b, &c);
            g[i][0]=a, g[i][1]=b, g[i][2]=c;
            addedge(a,b);
            addedge(b,a);
        }
        dfs1(1, 1, 0);
        getPOS(1, 1);
        build(1, n, 1);
        for(int i=1;i<=n;i++)
        {
            if(dep[g[i][0]] > dep[g[i][1]])
                swap(g[i][0], g[i][1]);
           // cout<<p[g[i][1]]<< ' '<< g[i][1]<<endl;
            update(p[g[i][1]], g[i][2]);
           // prt(p[g[i][1]]); prt(g[i][2]);
        }
        char op[11];
        while(scanf("%s", op)==1)
        {
            if(op[0]=='Q')
            {
                int a, b;
                //scanf("%d%d", &a, &b);
                read(a); read(b);
               // show(1, n, 1);
                printf("%d\n", find(a,b));
            }
            else if(op[0]=='C')
            {
                int a,b;
                //scanf("%d%d", &a, &b);
                read(a); read(b);

                update(p[g[a][1]], b, 1, n, 1);
               // show(1, n, 1);
            }
            else if(op[0]=='D')
            {
                putchar(10);
                break;
            }
        }
    }
    return 0;
}