This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <iostream>
#include <fstream>
#include <iomanip>
#include <algorithm>
#include <functional>
#include <numeric>
#include <cstring>
#include <string>
#include <cmath>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>
using namespace std;
#define ll long long
#define ull unsigned long long
#define f first
#define s second
#define PF push_front
#define PB push_back
#define MP make_pair
#define max(a, b) ((a > b)? a : b)
#define min(a, b) ((a < b)? a : b)
#define max3(a, b, c) max(max(a, b), c)
#define min3(a, b, c) min(min(a, b), c)
const int N = 2e5 + 5;
const int M = 1e9 + 7;
const int inf = 0x3f3f3f3f;
const ll int INF = 1e18;
struct BIT {
int sz;
vector<int> tree;
BIT(int n) : sz(n+1), tree(n+1, 0) {};
void add(int pos, int val){
for(; pos < sz; pos += pos&-pos) tree[pos] += val;
}
int sum(int pos){
int ans = 0;
for(; pos >= 1; pos -= pos&-pos) ans += tree[pos];
return ans;
}
};
vector<vector<pair<int, int>>> adj(N, vector<pair<int, int>>());
vector<vector<int>> par(20, vector<int>(N));
vector<pair<int, int>> ticket(N);
vector<int> to(N), to_edge(N), tin(N), tout(N);
int timer = 1;
void dfs(int cur, int prev){
tin[cur] = timer++;
for(auto [child, edge_id] : adj[cur]){
if(child == prev) continue;
to[child] = cur;
to_edge[child] = edge_id;
dfs(child, cur);
}
tout[cur] = timer++;
}
bool isAncestor(int anc, int child){
return (tin[anc] <= tin[child] && tout[anc] >= tout[child]);
}
int get_lca(int a, int b){
if(isAncestor(a, b)) return a;
int lca = b, cur = a;
for(int i = 19; i >= 0; i--){
int next_cur = par[i][cur];
if(isAncestor(next_cur, b)){
lca = next_cur;
}else {
cur = next_cur;
}
}
return lca;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
// ifstream cin();
// ofstream cout();
int n;
cin >> n;
for(int i = 1; i <= n-1; i++){
int a, b, c1, c2;
cin >> a >> b >> c1 >> c2;
adj[a].PB(MP(b, i));
adj[b].PB(MP(a, i));
ticket[i] = MP(c1, c2);
}
to[1] = 1;
to_edge[1] = -1;
dfs(1, -1);
BIT bit(n*2);
for(int i = 1; i <= n; i++) par[0][i] = to[i];
for(int i = 1; i < 20; i++){
for(int j = 1; j <= n; j++){
par[i][j] = par[i-1][par[i-1][j]];
}
}
for(int i = 1; i < n; i++){
int lca = get_lca(i, i+1);
bit.add(tin[i], 1);
bit.add(tin[i+1], 1);
bit.add(tin[lca], -2);
}
// Check for each edge, its number of passing
ll ans = 0;
for(int i = 2; i <= n; i++){
int cur = bit.sum(tout[i]) - bit.sum(tin[i] - 1), ind = to_edge[i];
ans += min(1ll * ticket[ind].f * cur, ticket[ind].s);
}
cout << ans << endl;
}
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