#include <bits/stdc++.h>
using namespace std;
#define int long long
#define FOR(i,s,e) for(int i = s; i <= (int)e; ++i)
#define DEC(i,s,e) for(int i = s; i >= (int)e; --i)
#define IAMSPEED ios_base::sync_with_stdio(false); cin.tie(0);
#ifdef LOCAL
#define db(x) cerr << #x << "=" << x << "\n"
#define db2(x, y) cerr << #x << "=" << x << " , " << #y << "=" << y << "\n"
#define db3(a,b,c) cerr<<#a<<"="<<a<<","<<#b<<"="<<b<<","<<#c<<"="<<c<<"\n"
#define dbv(v) cerr << #v << ":"; for (auto ite : v) cerr << ite << ' '; cerr <<"\n"
#define dbvp(v) cerr << #v << ":"; for (auto ite : v) cerr << "{" << ite.f << ',' << ite.s << "} "; cerr << "\n"
#define dba(a,ss,ee) cerr << #a << ":"; FOR(ite,ss,ee) cerr << a[ite] << ' '; cerr << "\n"
#define reach cerr << "LINE: " << __LINE__ << "\n";
#else
#define reach
#define db(x)
#define db2(x,y)
#define db3(a,b,c)
#define dbv(v)
#define dbvp(v)
#define dba(a,ss,ee)
#endif
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define pb push_back
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define f first
#define s second
#define g0(x) get<0>(x)
#define g1(x) get<1>(x)
#define g2(x) get<2>(x)
#define g3(x) get<3>(x)
typedef pair <int, int> pi;
typedef tuple<int,int,int> ti3;
typedef tuple<int,int,int,int> ti4;
int rand(int a, int b) { return a + rng() % (b-a+1); }
const int MOD = 1e9 + 7;
const int inf = (int)1e9 + 500;
const long long oo = (long long)1e18 + 500;
template <typename T> bool chmax(T& a, const T b) { return a<b ? a = b, 1 : 0; }
template <typename T> bool chmin(T& a, const T b) { return a>b ? a = b, 1 : 0; }
const int MAXN = 100005;
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt,tune=native")
int A[MAXN];
int n;
vector<pi> adj[MAXN];
int lvl[MAXN];
int sz[MAXN];
int par[MAXN];
int dist[MAXN][18]; // dist from the centroid of this level
int dfs_sz(int x, int p) {
sz[x] = 1;
for(auto v:adj[x]) {
if(v.f == p || lvl[v.f] != -1)continue;
sz[x]+=dfs_sz(v.f,x);
}
return sz[x];
}
int dfs2(int x, int p, int S) {
//trying to find the centroid
for(auto v:adj[x]){
if(v.f == p || lvl[v.f] != -1)continue;
if(sz[x] > S/2)return dfs2(v.f,x,S);
}
return x;
}
vector<pi> vec;
void dfs3(int x, int p, int l, int mx) {
// do stuff
for(auto v:adj[x]) {
if(v.f == p || lvl[v.f] != -1)continue;
dist[v.f][l] = dist[x][l] - v.s + A[v.f];
dfs3(v.f, x, l, max(mx, dist[v.f][l]));
}
// this is the start point
if(dist[x][l] >= mx) {
vec.pb({dist[x][l],1});
}
}
int ans;
void dfs4(int x, int p, int l, int mn){
for(auto v:adj[x]) {
if(v.f == p || lvl[v.f] != -1)continue;
dist[v.f][l] = dist[x][l] - v.s + A[v.f];
dfs4(v.f,x,l,min(mn, dist[v.f][l] - A[v.f]));
}
vec.pb({abs(mn),-1});
}
void build(int x, int p, int l) {
int s=dfs_sz(x,p);
int cent = dfs2(x,p,s);
if(p == -1) p = cent;
//fw::update(A[cent], 1);
vector<pi> V;
V.pb({A[cent],1});
V.pb({0,-1});
for(auto v:adj[cent]){
if(v.f == p || lvl[v.f] != -1)continue;
dist[v.f][l] = -v.s+A[v.f];
dfs4(v.f,cent,l,min(0ll, -v.s)); // consider this to be the end point
dist[v.f][l]=A[cent] - v.s + A[v.f];
dfs3(v.f,cent,l,max(A[cent],dist[v.f][l])); // consider this to be the start point
int c=0;
sort(all(vec),[](pi x, pi y) {
if(x.f!=y.f)return x.f>y.f;
else return x.s>y.s;
});
for(auto i:vec) {
if(i.s==1)++c;
else ans-=c; // double counted
}
for(auto i:vec)V.pb(i);
vec.clear();
}
ans--; // centroid paired with itself;
sort(all(V),[](pi x, pi y) {
if(x.f!=y.f)return x.f>y.f;
else return x.s>y.s;
});
int cnt = 0;
for(auto i:V) {
if(i.s==1)++cnt;
else ans+=cnt;
}
par[cent] = p;
lvl[cent] = l;
for(auto v:adj[cent]) {
if(lvl[v.f] != -1)continue;
build(v.f, cent, l+1);
}
}
int32_t main()
{
IAMSPEED
memset(lvl,-1,sizeof lvl);
cin >> n;
FOR(i,1,n) cin >> A[i];
FOR(i,1,n-1) {
int a,b,c; cin >> a >> b >> c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
build(1,-1,0);
cout << ans;
return (0-0) ;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
19 ms |
5056 KB |
Output is correct |
| 2 |
Correct |
80 ms |
9700 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
10 ms |
4820 KB |
Output is correct |
| 2 |
Correct |
11 ms |
5092 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
129 ms |
17600 KB |
Output is correct |
| 2 |
Correct |
96 ms |
15836 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
145 ms |
22988 KB |
Output is correct |
| 2 |
Correct |
191 ms |
25104 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
219 ms |
29724 KB |
Output is correct |
| 2 |
Correct |
268 ms |
34648 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
859 ms |
43180 KB |
Output is correct |
| 2 |
Correct |
936 ms |
50712 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
814 ms |
65536 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
723 ms |
39240 KB |
Output is correct |
| 2 |
Correct |
597 ms |
33044 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
967 ms |
48788 KB |
Output is correct |
| 2 |
Correct |
789 ms |
35564 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
831 ms |
65536 KB |
Execution killed with signal 9 |
| 2 |
Halted |
0 ms |
0 KB |
- |
