Submission #303932

#	Time	Username	Problem	Language	Result	Execution time	Memory
303932		BorisBarca	Harbingers (CEOI09_harbingers)	C++14	0 / 100	632 ms	65540 KiB

harbingers

/*
$$$$$$$\                      $$\           $$$$$$$\
$$  __$$\                     \__|          $$  __$$\
$$ |  $$ | $$$$$$\   $$$$$$\  $$\  $$$$$$$\ $$ |  $$ | $$$$$$\   $$$$$$\   $$$$$$$\ $$$$$$\
$$$$$$$\ |$$  __$$\ $$  __$$\ $$ |$$  _____|$$$$$$$\ | \____$$\ $$  __$$\ $$  _____|\____$$\
$$  __$$\ $$ /  $$ |$$ |  \__|$$ |\$$$$$$\  $$  __$$\  $$$$$$$ |$$ |  \__|$$ /      $$$$$$$ |
$$ |  $$ |$$ |  $$ |$$ |      $$ | \____$$\ $$ |  $$ |$$  __$$ |$$ |      $$ |     $$  __$$ |
$$$$$$$  |\$$$$$$  |$$ |      $$ |$$$$$$$  |$$$$$$$  |\$$$$$$$ |$$ |      \$$$$$$$\\$$$$$$$ |
\_______/  \______/ \__|      \__|\_______/ \_______/  \_______|\__|       \_______|\_______|
*/
#include <bits/stdc++.h>

using namespace std;

#define PB push_back
#define MP make_pair
#define INS insert
#define LB lower_bound
#define UB upper_bound
#define pii pair <int,int>
#define pll pair <long long, long long>
#define X first
#define Y second
#define _ << " " <<
#define sz(x) (int)x.size()
#define all(a) (a).begin(),(a).end()
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define FORD(i, a, b) for (int i = (a); i > (b); --i)
#define FORA(i, x) for (auto &i : x)
#define REP(i, n) FOR(i, 0, n)
#define BITS(x) __builtin_popcount(x)
#define SQ(a) (a) * (a)
#define TRACE(x) cout << #x " = " << (x) << '\n';
#define YES cout << "YES\n"
#define NO cout << "NO\n"
#define umap unordered_map

typedef long long ll;
typedef long double ld;
typedef vector <int> vi;
typedef vector <pii> vpi;
typedef vector <ll> vll;
typedef vector <pll> vpl;
typedef vector <double> vd;
typedef vector <ld> vld;
typedef vector<string> vs;
//((float) t)/CLOCKS_PER_SEC

const int MOD = 1e9 + 7;
const double PI = acos(-1);
const int INF = 1e9 + 10;
const ll INFL = 2e12 + 10;
const int ABC = 30;
const int dx[] = {-1, 1, 0, 0};
const int dy[] = {0, 0, -1, 1};
const int dox[] = {-1, 1, 0, 0, -1, -1, 1, 1};
const int doy[] = {0, 0, -1, 1, -1, 1, -1, 1};

inline int sum(int a, int b){
	if (a + b < 0)
		return (a + b + MOD) % MOD;
	return (a + b) % MOD;
}

inline void add(int &a, int b){
	a = sum(a, b);
}

inline int mul(ll a, ll b){
	return ((a % MOD) * ((ll)b % MOD)) % MOD;
}

inline int sub(int a, int b){
	return (a - b + MOD) % MOD;
}

inline int fast_pot(ll pot, ll n){
	ll ret = 1;
	while (n){
		if (n & 1LL)
			ret = (ret * pot) % MOD;
		pot = (pot * pot) % MOD;
		n >>= 1LL;
	}
	return ret;
}

inline int divide(int a, int b){
	return mul(a, fast_pot(b, MOD - 2));
}

ll lcm(ll a, ll b){
	return abs(a * b) / __gcd(a, b);
}

inline double ccw(pii A, pii B, pii C){
	return (A.X * B.Y) - (A.Y * B.X) + (B.X * C.Y) - (B.Y * C.X) + (C.X * A.Y) - (C.Y * A.X);
}

inline int CCW(pii A, pii B, pii C){
	double val = ccw(A, B, C);
	double eps = max(max(abs(A.X), abs(A.Y)), max(max(abs(B.X), abs(B.Y)), max(abs(C.X), abs(C.Y)))) / 1e9;
	if (val <= -eps)
		return -1;
	if (val >= eps)
		return 1;
	return 0;
}

void to_upper(string &x){
	REP(i, sz(x))
		x[i] = toupper(x[i]);
}

void to_lower(string &x){
	REP(i, sz(x))
		x[i] = tolower(x[i]);
}

string its(ll x){
	if (x == 0)
		return "0";
	string ret = "";
	while (x > 0){
		ret += (x % 10) + '0';
		x /= 10;
	}
	reverse(all(ret));
	return ret;
}

ll sti(string s){
	ll ret = 0;
	REP(i, sz(s)){
		ret *= 10;
		ret += (s[i] - '0');
	}
	return ret;
}

const ll M = 1e9 + 1;
const int N = 1e5 + 10;

struct pravac{
	ll a, b;
};

ll f(pravac p, ll x){
	return p.a * x + p.b;
}

struct node {
	pravac p;
	node *l, *r;	
	int vrijeme = 0;

	node(){
		l = r = NULL;
		p.a = 0, p.b = INFL;
	}

} *root;


ll n, st[N], dp[N], r[N], s[N], v[N];
vpl e[N];
int idx = 1;

struct LiChao{
	vector <node*> roots;
	map <ll, bool> need;
	int off;

	void init(ll n, ll v[]){
		for (off = 1; off < M; off *= 2);
		root = new node();
		FOR(i, 2, n + 1)
			popuni(v[i]);
		build(root, 1);
		roots.PB(root);
	}

	void popuni(int x){
		need[x + off] = 1;
		for (int i = (x + off) / 2; i > 0; i /= 2){
			//cout << i << '\n';
			need[i] = 1;
		}
	}

	void build(node *cvor, int id){
		if (!need[id])
			return;
		pravac p; p.a = 0, p.b = 0;
		cvor -> p = p;
		if (need[id * 2]){
			cvor -> l = new node();
			build(cvor -> l, id * 2);	
		}
		if (need[id * 2 + 1]){
			cvor -> r = new node();
			build(cvor -> r, id * 2 + 1);
		}
	}

	node *update(node *cvor, int lo, int hi, pravac p){
		node *novi = new node();
		if (cvor != NULL)
			*novi = *cvor;
		cvor = novi;

		// if (cvor -> l != NULL)
		// 	cvor -> l -> p = cvor -> p;
		// if (cvor -> r != NULL)
		// 	cvor -> r -> p = cvor -> p;

		int m = (lo + hi) / 2;
		//cout << m _ cvor -> p.a _ cvor -> p.b << '\n';
		bool left = (f(p, lo) < f(cvor -> p, lo));
		bool mid = (f(p, m) < f(cvor -> p, m));
		if (mid)
			cvor -> p = p;


		if (hi - lo == 1)
			return cvor;
		if (left != mid){
			if (cvor -> l != NULL)
				cvor -> l = update(cvor -> l, lo, m, p);
		}	else {
			if (cvor -> r != NULL)
				cvor -> r = update(cvor -> r, m, hi, p);
		}
		return cvor;
	}

	ll query(node *cvor, int lo, int hi, ll x){
		int m = (lo + hi) / 2;
		ll curr = f(cvor -> p, x);
		if (hi - lo == 1)
			return curr;

		// if (cvor -> l != NULL)
		// 	cvor -> l -> p = cvor -> p;
		// if (cvor -> r != NULL)
		// 	cvor -> r -> p = cvor -> p;

		if (x < m){
			if (cvor -> l == NULL)
				return curr;
			return min(curr, query(cvor -> l, lo, m, x));
		} else {
			if (cvor -> r == NULL)
				return curr;
			return min(curr, query(cvor -> r, m, hi, x));
		}
	}

	ll get(ll x){
		return query(roots.back(), 1, M, x);
	}

	void Add(pravac p){
		roots.PB(update(roots.back(), 1, M, p));
	}

	void roll_back(int t){
		assert(t <= sz(roots));
		roots.resize(t);
	}

} T;

void dfs(int node, int dad){
	st[node] = idx++;
	FORA(nxt, e[node]){
		if (nxt.X == dad)
			continue;
		dfs(nxt.X, node);
	}
}

void solve(int node, int dad, ll l, int k){
	if (dad != -1)
		dp[node] = s[node] + v[node] * l + T.get(v[node]);
	dp[node] = min(dp[node], v[node] * l + s[node]);

	//if (dad != -1){
		pravac p;
		p.a = -l, p.b = dp[node];
		T.Add(p);
	//}

	FORA(nxt, e[node]){
		if (nxt.X == dad)
			continue;
		T.roll_back(k);
		solve(nxt.X, node, l + nxt.Y, k + 1);
	}
}

// void test(){
// 	T.init(M);
// 	pravac p;
// 	p.a = -20, p.b = 206;
// 	T.Add(p);
// 	//cout << T.get(30) << '\n';
// }

int main () {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);

	//test();

	cin >> n;

	REP(i, n - 1){
		int x, y; cin >> x >> y;
		ll w; cin >> w;
		e[x].PB({y, w});
		e[y].PB({x, w});
	}	

	FOR(i, 2, n + 1)
		cin >> s[i] >> v[i];

	T.init(n, v);

	dfs(1, -1);
	solve(1, -1, 0, 1);

	FOR(i, 2, n + 1)
		cout << dp[i] << ' ';
	cout << '\n';

	return 0;
}

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