#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
using str = string; // yay python!
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
#define tcT template<class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>;
tcT, size_t SZ> using AR = array<T,SZ>;
tcT> using PR = pair<T,T>;
// pairs
#define mp make_pair
#define f first
#define s second
// vectors
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18; // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
const int dx[4] = {1,0,-1,0}, dy[4] = {0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;
// helper funcs
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down
tcT> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
tcTU> T fstTrue(T lo, T hi, U f) {
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo+(hi-lo)/2;
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
lo --; assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo+(hi-lo+1)/2;
f(mid) ? lo = mid : hi = mid-1;
}
return lo;
}
tcT> void remDup(vector<T>& v) { // sort and remove duplicates
sort(all(v)); v.erase(unique(all(v)),end(v)); }
tcTU> void erase(T& t, const U& u) { // don't erase
auto it = t.find(u); assert(it != end(t));
t.erase(u); } // element that doesn't exist from (multi)set
// INPUT
#define tcTUU tcT, class ...U
tcT> void re(complex<T>& c);
tcTU> void re(pair<T,U>& p);
tcT> void re(vector<T>& v);
tcT, size_t SZ> void re(AR<T,SZ>& a);
tcT> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
tcTUU> void re(T& t, U&... u) { re(t); re(u...); }
tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; }
tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
tcT> void re(vector<T>& x) { trav(a,x) re(a); }
tcT, size_t SZ> void re(AR<T,SZ>& x) { trav(a,x) re(a); }
tcT> void rv(int& n, vector<T>& x) { re(n); x.rsz(n); trav(a,x) re(a); }
// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
return b ? "true" : "false";
#else
return ts((int)b);
#endif
}
tcT> str ts(complex<T> c) {
stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
tcTU> str ts(pair<T,U> p);
tcT> str ts(T v) { // containers with begin(), end()
#ifdef LOCAL
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
#else
bool fst = 1; str res = "";
for (const auto& x: v) {
if (!fst) res += " ";
fst = 0; res += ts(x);
}
return res;
#endif
}
tcTU> str ts(pair<T,U> p) {
#ifdef LOCAL
return "("+ts(p.f)+", "+ts(p.s)+")";
#else
return ts(p.f)+" "+ts(p.s);
#endif
}
// OUTPUT
tcT> void pr(T x) { cout << ts(x); }
tcTUU> void pr(const T& t, const U&... u) {
pr(t); pr(u...); }
void ps() { pr("\n"); } // print w/ spaces
tcTUU> void ps(const T& t, const U&... u) {
pr(t); if (sizeof...(u)) pr(" "); ps(u...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU> void DBG(const T& t, const U&... u) {
cerr << ts(t); if (sizeof...(u)) cerr << ", ";
DBG(u...); }
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
#define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
<< __FUNCTION__ << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif
// FILE I/O
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
/**
* Description: LiChao Segment Tree
* Source: atatomir, misc
* Verification: CSA Squared Ends
* https://judge.yosupo.jp/problem/segment_add_get_min
*/
struct Line {
int k; ll m;
Line(int _k, ll _m) { k = _k, m = _m; }
Line() : Line(0,LLONG_MIN) { }
ll get(ll x) { return k*x+m; }
bool majorize(Line X, ll L, ll R) {
return get(L) >= X.get(L) && get(R) >= X.get(R); }
};
// struct lc {
// lc* c[2]; Line S;
// lc() { c[0] = c[1] = NULL; S = Line(); }
// ~lc() { F0R(i,2) delete c[i]; }
// void mc(int i) { if (!c[i]) c[i] = new lc(); }
// ll mid(ll x) { return x&1?(x-1)/2:x/2; }
// ll query(ll X, ll L, ll R) {
// ll ans = S.get(X), M = mid(L+R);
// if (X <= M) {
// if (c[0]) ckmax(ans,c[0]->query(X,L,M));
// } else {
// if (c[1]) ckmax(ans,c[1]->query(X,M+1,R));
// }
// return ans;
// }
// void modify(Line X, ll L, ll R) {
// if (X.majorize(S,L,R)) swap(X,S);
// if (S.majorize(X,L,R)) return;
// if (S.get(L) < X.get(L)) swap(X,S);
// ll M = mid(L+R);
// if (X.get(M) >= S.get(M)) swap(X,S), mc(0), c[0]->modify(X,L,M);
// else mc(1), c[1]->modify(X,M+1,R);
// }
// void upd(Line X, ll lo, ll hi, ll L, ll R) {
// if (R < lo || hi < L) return;
// if (lo <= L && R <= hi) return modify(X,L,R);
// ll M = mid(L+R);
// if (lo <= M) mc(0), c[0]->upd(X,lo,hi,L,M);
// if (hi > M) mc(1), c[1]->upd(X,lo,hi,M+1,R);
// }
// };
Line dat[1<<17];
struct LC {
vi dists;
vpi st;
int seg[1<<18];
ll get(int x, int M) {
return dat[x].get(dists[M]);
}
bool majorize(int x, int y, int L, int R) {
return get(x,L) <= get(y,L) && get(x,R) <= get(y,R);
}
void upd(int x, int ind, int L, int R) {
if (majorize(x,seg[ind],L,R)) {
st.pb({ind,seg[ind]});
swap(x,seg[ind]);
}
if (majorize(seg[ind],x,L,R)) return;
if (get(seg[ind],L) > get(x,L)) {
st.pb({ind,seg[ind]});
swap(x,seg[ind]);
}
int M = (L+R)/2;
if (get(x,M) < get(seg[ind],M)) {
st.pb({ind,seg[ind]});
swap(x,seg[ind]), upd(x,2*ind,L,M);
} else upd(x,2*ind+1,M+1,R);
}
void upd(int num) {
upd(num,1,0,sz(dists)-1);
}
ll query(int pos, int ind, int L, int R) {
ll ans = LLONG_MAX;
ckmin(ans,get(seg[ind],pos));
if (L != R) {
int M = (L+R)/2;
if (pos <= M) ckmin(ans,query(pos,2*ind,L,M));
else ckmin(ans,query(pos,2*ind+1,M+1,R));
}
return ans;
}
ll query(int dist) {
int pos = lb(all(dists),dist)-begin(dists);
assert(dists[pos] == dist);
return query(pos,1,0,sz(dists)-1);
}
void rollback(int tmp) {
while (sz(st) > tmp) {
seg[st.bk.f] = st.bk.s;
st.pop_back();
}
}
};
LC lc;
vpi adj[1<<17];
int dist[1<<17],prep[1<<17],val[1<<17];
ll ans[1<<17];
int N;
vpi mods;
void dfs_ans(int x, int y = -1) {
if (x > 1) ans[x] = lc.query(val[x])+(ll)val[x]*dist[x]+prep[x];
int tmp = sz(lc.st);
dat[x] = {-dist[x],ans[x]};
lc.upd(x);
trav(t,adj[x]) if (t.f != y) {
dfs_ans(t.f,x);
}
lc.rollback(tmp);
}
void dfs_dist(int x, int y = -1, int tot = 0) {
dist[x] = tot;
trav(t,adj[x]) if (t.f != y) {
dfs_dist(t.f,x,tot+t.s);
}
}
int main() {
setIO(); re(N);
FOR(i,2,N+1) {
int u,v,d; re(u,v,d);
adj[u].pb({v,d}), adj[v].pb({u,d});
}
// dfs("AA");
FOR(i,2,N+1) re(prep[i],val[i]);
// dfs("BB");
dfs_dist(1);
FOR(i,2,N+1) lc.dists.pb(val[i]);
remDup(lc.dists);
dat[0] = Line(0,LLONG_MAX);
dfs_ans(1);
FOR(i,2,N+1) pr(ans[i],' ');
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
*/
Compilation message
harbingers.cpp: In function ‘void setIn(str)’:
harbingers.cpp:185:28: warning: ignoring return value of ‘FILE* freopen(const char*, const char*, FILE*)’, declared with attribute warn_unused_result [-Wunused-result]
185 | void setIn(str s) { freopen(s.c_str(),"r",stdin); }
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
harbingers.cpp: In function ‘void setOut(str)’:
harbingers.cpp:186:29: warning: ignoring return value of ‘FILE* freopen(const char*, const char*, FILE*)’, declared with attribute warn_unused_result [-Wunused-result]
186 | void setOut(str s) { freopen(s.c_str(),"w",stdout); }
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
5484 KB |
Output is correct |
| 2 |
Correct |
6 ms |
6252 KB |
Output is correct |
| 3 |
Correct |
93 ms |
18280 KB |
Output is correct |
| 4 |
Correct |
139 ms |
25036 KB |
Output is correct |
| 5 |
Correct |
171 ms |
28000 KB |
Output is correct |
| 6 |
Correct |
208 ms |
31960 KB |
Output is correct |
| 7 |
Correct |
108 ms |
17248 KB |
Output is correct |
| 8 |
Correct |
449 ms |
24656 KB |
Output is correct |
| 9 |
Correct |
211 ms |
29256 KB |
Output is correct |
| 10 |
Correct |
189 ms |
26948 KB |
Output is correct |
