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heavy_light_decomposition.cpp
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heavy_light_decomposition.cpp
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//
// Heavy-Light Decomposition
//
// verified:
// AOJ 2667 Tree
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2667
//
#include <iostream>
#include <functional>
#include <vector>
#include <queue>
#include <stack>
using namespace std;
// HL-Decomposition
// vid: id of v after HL-Decomposition
// inv: inv[vid[v]] = v
// par: id of parent
// depth
// subsize: size of subtree
// head: head-id in the heavy-path
// prev, next: prev-id, next-id in the heavy-path
// type: the id of tree for forest
// vend: the last-id of node in v-subtree
typedef vector<vector<int> > Graph;
struct HLDecomposition {
int n;
Graph G;
vector<int> vid, inv, par, depth, subsize, head, prev, next, type;
// construct
HLDecomposition() { }
HLDecomposition(const Graph &G_) :
n((int)G_.size()), G(G_),
vid(n, -1), inv(n), par(n), depth(n), subsize(n, 1),
head(n), prev(n, -1), next(n, -1), type(n) { }
void build(vector<int> roots = {0}) {
int curtype = 0, pos = 0;
for (auto r : roots) decide_heavy_edge(r), reconstruct(r, curtype++, pos);
}
void decide_heavy_edge(int r) {
stack<pair<int,int> > st;
par[r] = -1, depth[r] = 0;
st.emplace(r, 0);
while (!st.empty()) {
int v = st.top().first;
int &i = st.top().second;
if (i < (int)G[v].size()) {
int e = G[v][i++];
if (e == par[v]) continue;
par[e] = v, depth[e] = depth[v] + 1;
st.emplace(e, 0);
}
else {
st.pop();
int maxsize = 0;
for (auto e : G[v]) {
if (e == par[v]) continue;
subsize[v] += subsize[e];
if (maxsize < subsize[e]) maxsize = subsize[e], prev[e] = v, next[v] = e;
}
}
}
}
void reconstruct(int r, int curtype, int &pos) {
stack<int> st({r});
while (!st.empty()) {
int start = st.top(); st.pop();
for (int v = start; v != -1; v = next[v]) {
type[v] = curtype;
vid[v] = pos++;
inv[vid[v]] = v;
head[v] = start;
for (auto e : G[v]) if (e != par[v] && e != next[v]) st.push(e);
}
}
}
// node query [u, v], f([left, right])
void foreach_nodes(int u, int v, const function<void(int,int)> &f) {
while (true) {
if (vid[u] > vid[v]) swap(u, v);
f(max(vid[head[v]], vid[u]), vid[v]);
if (head[u] != head[v]) v = par[head[v]];
else break;
}
}
// edge query [u, v], f([left, right])
void foreach_edges(int u, int v, const function<void(int,int)> &f) {
while (true) {
if (vid[u] > vid[v]) swap(u, v);
if (head[u] != head[v]) {
f(vid[head[v]], vid[v]);
v = par[head[v]];
}
else {
if (u != v) {
f(vid[u]+1, vid[v]);
}
break;
}
}
}
// LCA
int lca(int u, int v) {
while (true) {
if (vid[u] > vid[v]) swap(u, v);
if (head[u] == head[v]) return u;
v = par[head[v]];
}
}
};
// BIT
template <class Abel> struct BIT {
vector<Abel> dat[2];
Abel UNITY_SUM = 0; // to be set
/* [1, n] */
BIT(int n) { init(n); }
void init(int n) { for (int iter = 0; iter < 2; ++iter) dat[iter].assign(n + 1, UNITY_SUM); }
/* a is 1-indexed */
inline void sub_add(int p, int a, Abel x) {
for (int i = a; i < (int)dat[p].size(); i += i & -i)
dat[p][i] = dat[p][i] + x;
}
inline void add(int a, int b, Abel x) {
sub_add(0, a, x * -(a - 1)); sub_add(1, a, x); sub_add(0, b, x * (b - 1)); sub_add(1, b, x * (-1));
}
/* [1, a], a is 1-indexed */
inline Abel sub_sum(int p, int a) {
Abel res = UNITY_SUM;
for (int i = a; i > 0; i -= i & -i) res = res + dat[p][i];
return res;
}
inline Abel sum(int a, int b) {
return sub_sum(0, b - 1) + sub_sum(1, b - 1) * (b - 1) - sub_sum(0, a - 1) - sub_sum(1, a - 1) * (a - 1);
}
/* debug */
void print() {
for (int i = 1; i < (int)dat[0].size(); ++i) cout << sum(i, i + 1) << ",";
cout << endl;
}
};
//------------------------------//
// Examples
//------------------------------//
/* AOJ 2667 Tree */
int main() {
int N, Q; cin >> N >> Q;
Graph G(N);
for (int i = 0; i < N-1; ++i) {
int u, v; scanf("%d %d", &u, &v);
G[u].push_back(v); G[v].push_back(u);
}
HLDecomposition hld(G);
hld.build();
BIT<long long> bit(N+1);
for (int q = 0; q < Q; ++q) {
int type, a, b; scanf("%d %d %d", &type, &a, &b);
if (type == 0) {
long long res = 0;
// ∂Ë¥÷œ¬ºË∆¿
hld.foreach_edges(a, b, [&](int l, int r){ res += bit.sum(l, r+1); });
cout << res << endl;
}
else {
// …Ù ¨Ã⁄§Œ§ §π∂Ë¥÷§À b §Ú≤√ªª
bit.add(hld.vid[a]+1, hld.vid[a]+hld.subsize[a], b);
}
}
}