Submission #237143

#	Time	Username	Problem	Language	Result	Execution time	Memory
237143		xiaowuc1	Harbingers (CEOI09_harbingers)	C++14	100 / 100	133 ms	19192 KiB

harbingers

#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <vector>

using namespace std;

// BEGIN NO SAD
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define trav(a, x) for(auto& a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x).size()
typedef vector<int> vi;
// END NO SAD

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<vector<ll>> matrix;
typedef pair<ll, ll> pll;

int n;
vector<pii> edges[100005];
ll ret[100005];
ll dist[100005];
ll gain[100005];
ll timeper[100005];

pll bestlines[100005]; // bestlines.first * x + bestlines.second
int numlines;

ll eval(pll a, ll x) {
  return a.first*x + a.second;
}

ll qry(ll x) {
  assert(numlines > 0);
  int lhs = 0;
  int rhs = numlines-1;
  while(lhs != rhs) {
    int mid = (lhs+rhs)/2;
    if(eval(bestlines[mid], x) <= eval(bestlines[mid+1], x)) rhs = mid;
    else lhs = mid + 1;
  }
  ll ret = eval(bestlines[lhs], x);
  return ret;
}

bool cross(pll a, pll b, pll c){
  return (1.0 * (b.second - a.second) / (a.first - b.first) >= 1.0 * (c.second - b.second) / (b.first - c.first));
}

int ins(pll a) {
  if(numlines <= 1) return numlines;
  int lhs = 0;
  int rhs = numlines-1;
  while(lhs != rhs) {
    int mid = (lhs+rhs)/2;
    if(cross(bestlines[mid], bestlines[mid+1], a)) rhs = mid;
    else lhs = mid+1;
  }
  return lhs+1;
}

void dfs(int curr, int par) {
  if(curr > 1) {
    ret[curr] = gain[curr] + timeper[curr]*dist[curr] + qry(timeper[curr]);
  }
  int oldnumlines = numlines;
  int idx = ins(pll(-dist[curr], ret[curr]));
  pll save = bestlines[idx];
  for(pii out: edges[curr]) {
    if(out.first == par) continue;
    numlines = idx+1;
    bestlines[idx] = pll(-dist[curr], ret[curr]);
    dist[out.first] = dist[curr] + out.second;
    dfs(out.first, curr);
  }
  bestlines[idx] = save;
  numlines = oldnumlines;
}

void solve() {
  cin >> n;
  for(int i = 1; i < n; i++) {
    int a, b, w;
    cin >> a >> b >> w;
    edges[a].emplace_back(b, w);
    edges[b].emplace_back(a, w);
  }
  for(int i = 2; i <= n; i++) cin >> gain[i] >> timeper[i];
  dfs(1, -1);
  for(int i = 2; i <= n; i++) cout << ret[i] << " \n"[i == n];
}

// are there edge cases (N=1?)
// are array sizes proper (scaled by proper constant, for example 2* for koosaga tree)
// integer overflow?
// DS reset properly between test cases

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL); cout.tie(NULL);
  solve();
}

• Subtask 1: 100 / 100