树链剖分
- 给\(x->y\)结点最短路径上所有节点的值都加上\(z\)
- 求\(x->y\)结点最短路径上所有节点的值之和
- 给\(x\)为根节点的子树内所有节点值都加上\(z\)
- 求以\(x\)为根节点的子树内所有节点值和
P3384 【模板】轻重链剖分
#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
#define DOF 0x7f7f7f7f
#define endl '\n'
#define mem(a, b) memset(a, b, sizeof(a))
#define debug(case, x) cout << case << " : " << x << endl
#define open freopen("ii.txt", "r", stdin)
#define close freopen("oo.txt", "w", stdout)
#define IO \
ios::sync_with_stdio(false); \
cin.tie(0); \
cout.tie(0)
#define pb push_back
using namespace std;
//#define int long long
#define lson rt << 1
#define rson rt << 1 | 1
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<long long, long long> PII;
const int maxn = 2e5 + 10;
int n, m, r, mod;
int head[maxn], tot;
struct edge {
int to, next;
} edge[maxn];
int w[maxn], wt[maxn];
//w输入时的权值，wt编号后的权值
int son[maxn], id[maxn], fa[maxn], dep[maxn], sz[maxn], top[maxn], cnt = 0;
//son重儿子、id新编号、fa父亲节点、dep深度、sz子树大小、top顶端、cnt标号。
void add(int u, int v) {
edge[++tot].to = v;
edge[tot].next = head[u];
head[u] = tot;
}
struct SegTree {
int tree[maxn << 2], lazy[maxn << 2];
void push_down(int rt, int len) {
if(lazy[rt]) {
lazy[lson] += lazy[rt];
lazy[rson] += lazy[rt];
tree[lson] += lazy[rt] * (len - len / 2);
tree[rson] += lazy[rt] * (len / 2);
tree[lson] %= mod;
tree[rson] %= mod;
lazy[rt] = 0;
}
}
void build(int rt, int l, int r) {
if(l == r) {
tree[rt] = wt[l];
tree[rt] %= mod;
return ;
}
int mid = (l + r) >> 1;
build(lson, l, mid);
build(rson, mid + 1, r);
tree[rt] = (tree[lson] + tree[rson]) % mod;
}
int query(int rt, int l, int r, int L, int R) {
if(L <= l && r <= R) {
return tree[rt];
}
push_down(rt, r - l + 1);
int mid = (l + r) >> 1, res = 0;
if(L <= mid)
res = (res + query(lson, l, mid, L, R)) % mod;
if(R > mid)
res = (res + query(rson, mid + 1, r, L, R)) % mod;
return res;
}
void update(int rt, int l, int r, int L, int R, int k) {
if(L <= l && r <= R) {
lazy[rt] += k;
tree[rt] += k * (r - l + 1);
return ;
}
push_down(rt, r - l + 1);
int mid = (l + r) >> 1;
if(L <= mid)
update(lson, l, mid, L, R, k);
if(R > mid)
update(rson, mid + 1, r, L, R, k);
tree[rt] = (tree[lson] + tree[rson]) % mod;
}
} s_t;
int query(int x, int y) {
int res = 0;
while(top[x] != top[y]) {
if(dep[top[x]] < dep[top[y]])swap(x, y);
res += s_t.query(1, 1, n, id[top[x]], id[x]);
res %= mod;
x = fa[top[x]];
}
if(dep[x] > dep[y])swap(x, y);
res += s_t.query(1, 1, n, id[x], id[y]);
res %= mod;
return res;
}
void update(int x, int y, int k) {
while(top[x] != top[y]) {
if(dep[top[x]] < dep[top[y]])swap(x, y);
s_t.update(1, 1, n, id[top[x]], id[x], k);
x = fa[top[x]];
}
if(dep[x] > dep[y])swap(x, y);
s_t.update(1, 1, n, id[x], id[y], k);
}
int query_son(int x) {
int res = 0;
res += s_t.query(1, 1, n, id[x], id[x] + sz[x] - 1);
res %= mod;
return res;
}
void update_son(int x, int k) {
s_t.update(1, 1, n, id[x], id[x] + sz[x] - 1, k);
}
void dfs1(int u, int father) {
dep[u] = dep[father] + 1;
sz[u] = 1;
fa[u] = father;
int maxson = -1;
for(int i = head[u]; i; i = edge[i].next) {
int v = edge[i].to;
if(v == father)continue;
dfs1(v, u);
sz[u] += sz[v];
if(sz[v] > maxson)
son[u] = v, maxson = sz[v];
}
}
void dfs2(int u, int topf) {
id[u] = ++cnt;
wt[cnt] = w[u];
top[u] = topf;
if(!son[u]) return ;
dfs2(son[u], topf);
for(int i = head[u]; i; i = edge[i].next) {
int v = edge[i].to;
if(v == fa[u] || v == son[u]) continue;
dfs2(v, v);
}
}
int main() {
scanf("%d%d%d%d", &n, &m, &r, &mod);
for(int i = 1; i <= n; ++i)scanf("%d", &w[i]);
for(int i = 1; i < n; ++i) {
int x, y;
scanf("%d%d", &x, &y);
add(x, y);
add(y, x);
}
dfs1(r, 0);
dfs2(r, r);
s_t.build(1, 1, n);
while(m--) {
int k, x, y, z;
scanf("%d", &k);
if(k == 1) {
scanf("%d%d%d", &x, &y, &z);
update(x, y, z);
} else if(k == 2) {
scanf("%d%d", &x, &y);
printf("%d\n", query(x, y));
} else if(k == 3) {
scanf("%d%d", &x, &y);
update_son(x, y);
} else {
scanf("%d", &x);
printf("%d\n", query_son(x));
}
}
}
