樹鏈剖分

撿起來好久沒寫的樹剖。。。竟然沒有寫掛。。一次過了。。。
就是用線段樹來維護一顆樹上的dfs序

#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
#define full(a, b) memset(a, b, sizeof a)
using namespace std;
typedef long long ll;
inline int lowbit(int x){ return x & (-x); }
inline int read(){
    int X = 0, w = 0; char ch = 0;
    while(!isdigit(ch)) { w |= ch == '-'; ch = getchar(); }
    while(isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar();
    return w ? -X : X;
}
inline int gcd(int a, int b){ return a % b ? gcd(b, a % b) : b; }
inline int lcm(int a, int b){ return a / gcd(a, b) * b; }
template<typename T>
inline T max(T x, T y, T z){ return max(max(x, y), z); }
template<typename T>
inline T min(T x, T y, T z){ return min(min(x, y), z); }
template<typename A, typename B, typename C>
inline A fpow(A x, B p, C lyd){
    A ans = 1;
    for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;
    return ans;
}
const int N = 30005;
int n, cnt, dfn, head[N], depth[N], size[N], son[N], p[N], top[N], id[N], w[N], val[N];
int tree[N<<2], m[N<<2];
struct Edge { int v, next; } edge[N<<1];

void addEdge(int a, int b){
    edge[cnt].v = b, edge[cnt].next = head[a], head[a] = cnt ++;
}

void dfs1(int s, int fa){
    depth[s] = depth[fa] + 1;
    p[s] = fa;
    size[s] = 1;
    int child = -1;
    for(int i = head[s]; i != -1; i = edge[i].next){
        int u = edge[i].v;
        if(u == fa) continue;
        dfs1(u, s);
        size[s] += size[u];
        if(size[u] > child) child = size[u], son[s] = u;
    }
}

void dfs2(int s, int tp){
    id[s] = ++dfn;
    w[id[s]] = val[s];
    top[s] = tp;
    if(son[s] != -1) dfs2(son[s], tp);
    for(int i = head[s]; i != -1; i = edge[i].next){
        int u = edge[i].v;
        if(u == p[s] || u == son[s]) continue;
        dfs2(u, u);
    }
}

void push_up(int rt){
    tree[rt] = tree[rt << 1] + tree[rt << 1 | 1];
    m[rt] = max(m[rt << 1], m[rt << 1 | 1]);
}

void buildTree(int rt, int l, int r){
    if(l == r){
        tree[rt] = m[rt] = w[l];
        return;
    }
    int mid = (l + r) >> 1;
    buildTree(rt << 1, l, mid);
    buildTree(rt << 1 | 1, mid + 1, r);
    push_up(rt);
}

void modify(int rt, int l, int r, int k, int t){
    if(l == r){
        tree[rt] = m[rt] = t;
        return;
    }
    int mid = (l + r) >> 1;
    if(k <= mid) modify(rt << 1, l, mid, k, t);
    else modify(rt << 1 | 1, mid + 1, r, k, t);
    push_up(rt);
}

int queryMax(int rt, int l, int r, int queryL, int queryR){
    if(l == queryL && r == queryR){
        return m[rt];
    }
    int mid = (l + r) >> 1;
    if(queryL > mid) return queryMax(rt << 1 | 1, mid + 1, r, queryL, queryR);
    else if(queryR <= mid) return queryMax(rt << 1, l, mid, queryL, queryR);
    else return max(queryMax(rt << 1, l, mid, queryL, mid),
                    queryMax(rt << 1 | 1, mid + 1, r, mid + 1, queryR));
}

int querySum(int rt, int l, int r, int queryL, int queryR){
    if(l == queryL && r == queryR){
        return tree[rt];
    }
    int mid = (l + r) >> 1;
    if(queryL > mid) return querySum(rt << 1 | 1, mid + 1, r, queryL, queryR);
    else if(queryR <= mid) return querySum(rt << 1, l, mid, queryL, queryR);
    else return querySum(rt << 1, l, mid, queryL, mid) +
                querySum(rt << 1 | 1, mid + 1, r, mid + 1, queryR);
}

int treeMax(int x, int y){
    int ret = -INF;
    while(top[x] != top[y]){
        if(depth[top[x]] < depth[top[y]]) swap(x, y);
        ret = max(ret, queryMax(1, 1, n, id[top[x]], id[x]));
        x = p[top[x]];
    }
    if(depth[x] > depth[y]) swap(x, y);
    return max(ret, queryMax(1, 1, n, id[x], id[y]));
}

int treeSum(int x, int y){
    int ret = 0;
    while(top[x] != top[y]){
        if(depth[top[x]] < depth[top[y]]) swap(x, y);
        ret += querySum(1, 1, n, id[top[x]], id[x]);
        x = p[top[x]];
    }
    if(depth[x] > depth[y]) swap(x, y);
    ret += querySum(1, 1, n, id[x], id[y]);
    return ret;
}

int main(){

    full(head, -1);
    full(son, -1);
    n = read();
    for(int i = 0; i < n - 1; i ++){
        int u = read(), v = read();
        addEdge(u, v), addEdge(v, u);
    }
    for(int i = 1; i <= n; i ++) val[i] = read();
    dfs1(1, 0), dfs2(1, 1);
    buildTree(1, 1, n);
    int q = read();
    while(q --){
        char opt[10]; scanf("%s", opt);
        if(opt[1] == 'H'){
            int x = read(), y = read();
            modify(1, 1, n, id[x], y);
        }
        else if(opt[1] == 'M'){
            int x = read(), y = read();
            printf("%d\n", treeMax(x, y));
        }
        else if(opt[1] == 'S'){
            int x = read(), y = read();
            printf("%d\n", treeSum(x, y));
        }
    }
    return 0;
}
 

BZOJ 1036 樹的統計