思路：

用dfs序+线段树维护子树中距离（从1到u，再从u到1）的最小值

代码：

#pragma GCC optimize(2)#pragma GCC optimize(3)#pragma GCC optimize(4)#include
     
      using namespace std;#define fi first#define se second#define pi acos(-1.0)#define LL long long//#define mp make_pair#define pb push_back#define ls rt<<1, l, m#define rs rt<<1|1, m+1, r#define ULL unsigned LL#define pll pair
      
       #define pii pair
       
        #define piii pair
        
         #define mem(a, b) memset(a, b, sizeof(a))#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);#define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);//headconst int N = 2e5 + 5;const LL INF = 0x3f3f3f3f3f3f3f3f;int L[N], R[N], anc[N][20], deep[N], f[N], b[N], bb[N], head[N], cnt = 1, now = 1;LL tree[N<<2], lazy[N<<2], a[N];struct edge {    int from, to, w, nxt;}edge[N];void add_edge(int u, int v, int w) {    edge[cnt].from = u;    edge[cnt].to = v;    edge[cnt].w = w;    edge[cnt].nxt = head[u];    head[u] = cnt++;}void push_up(int rt) {    tree[rt] = min(tree[rt<<1], tree[rt<<1|1]);}void push_down(int rt) {    lazy[rt<<1] += lazy[rt];    lazy[rt<<1|1] += lazy[rt];    tree[rt<<1] += lazy[rt];    tree[rt<<1|1] += lazy[rt];    lazy[rt] = 0;}void build(int rt, int l, int r) {    if(l == r) {        tree[rt] = a[f[l]];        return ;    }    int m = l+r >> 1;    build(ls);    build(rs);    push_up(rt);}void update(int L, int R, int v, int rt, int l, int r) {    if(L <= l && r <= R) {        tree[rt] += v;        lazy[rt] += v;        return ;    }    if(lazy[rt]) push_down(rt);    int m = l+r >> 1;    if(L <= m) update(L, R, v, ls);    if(R > m) update(L, R, v, rs);    push_up(rt);}LL query(int L, int R, int rt, int l, int r) {    if(L <= l && r <= R) return tree[rt];    if(lazy[rt]) push_down(rt);    int m = l+r >> 1;    LL ans = INF;    if(L <= m) ans = min(ans, query(L, R, ls));    if(R > m) ans = min(ans, query(L, R, rs));    push_up(rt);    return ans;}void dfs(int u) {    L[u] = now;    f[now] = u;    for (int i = head[u]; ~i; i = edge[i].nxt) {        int v = edge[i].to;        anc[v][0] = u;        for (int j = 1; j < 20; j++) anc[v][j] = anc[anc[v][j-1]][j-1];        deep[v] = deep[u] + 1;        now++;        a[v] = a[u] - b[u] + edge[i].w + b[v];        dfs(v);    }    R[u] = now;}int lca(int u, int v) {    if(deep[u] < deep[v]) swap(u, v);    for (int i = 19; i >= 0; i--) if(deep[anc[u][i]] >= deep[v]) u = anc[u][i];    if(u == v) return u;    for (int i = 19; i >= 0; i--) if(anc[u][i] != anc[v][i]) u = anc[u][i], v = anc[v][i];    return anc[u][0];}int main() {    int n, q, ty, u, v, w;    mem(head, -1);    scanf("%d %d", &n, &q);    for (int i = 1; i < n; i++) {        scanf("%d %d %d", &u, &v, &w);        add_edge(u, v, w);    }    for (int i = 1; i < n; i++) {        scanf("%d %d %d", &u, &v, &w);        b[u] = w;        bb[i] = u;    }    for (int i = 0; i < 20; i++) anc[1][i] = 1;    dfs(1);    build(1, L[1], R[1]);    while(q--) {        scanf("%d %d %d", &ty, &u, &v);        if(ty == 1) {            if(u >= n) {                int nod = bb[u-n+1];                int add = v - b[nod];                update(L[nod], L[nod], add, 1, L[1], R[1]);                b[nod] = v;            }            else {                int nod = edge[u].to;                int add = v - edge[u].w;                update(L[nod], R[nod], add, 1, L[1], R[1]);                edge[u].w = v;            }        }        else {            int l = lca(u, v);            LL ans = INF;            if(l == u) {                LL dis1 = query(L[u], L[u], 1, L[1], R[1]) - b[u];                LL dis2 = query(L[v], L[v], 1, L[1], R[1]) - b[v];                ans = dis2 - dis1;            }            else {                LL dis1 = query(L[u], R[u], 1, L[1], R[1]) - (query(L[u], L[u], 1, L[1], R[1]) - b[u]);                LL dis2 = query(L[v], L[v], 1, L[1], R[1]) - b[v];                ans = dis1 + dis2;            }            printf("%lld\n", ans);        }    }    return 0;}