Submission #889623

#	Time	Username	Problem	Language	Result	Execution time	Memory
889623		asdfgrace	Race (IOI11_race)	C++17	0 / 100	13 ms	51344 KiB

race

#include <bits/stdc++.h>
#include "race.h"
using namespace std;

/*
start at the centroid
consider all paths whose lca is the centroid of the tree
try solving each of these in o(n)?
can we knapsack?
consider root & sum of weights on paths to each node
do a dfs
then for each node
search for a matching path
*/

multiset<int> at[1000010];

int best_path(int N, int K, int H[][2], int L[]) {
  int ans = 1e9;
  vector<vector<pair<int, int>>> edges(N);
  for (int i = 0; i < N - 1; i++) {
    edges[H[i][0]].push_back({H[i][1], L[i]});
    edges[H[i][1]].push_back({H[i][0], L[i]});
  }
  at[0].insert(0);
  vector<int> sz(N, 1), val(N, 0), dep(N, 0);
  vector<bool> visited(N, false);
  function<void(int, int)> dfs_sz = [&] (int node, int par) {
    sz[node] = 1;
    for (auto [next, wt] : edges[node]) {
      if (next == par || visited[next]) continue;
      dfs_sz(next, node);
      sz[node] += sz[next];
    }
  };
  function<int(int, int, int)> centroid = [&] (int node, int par, int s) {
    for (auto [next, wt] : edges[node]) {
      if (next != par && !visited[next] && sz[next] > s / 2) {
        return centroid(next, node, s);
      }
    }
    return node;
  };
  function<void(int, int)> dfs_val = [&] (int node, int par) {
    for (auto [next, wt] : edges[node]) {
      if (next != par && !visited[next]) {
        dep[next] = dep[node] + 1;
        val[next] = min(val[node] + wt, 1000005);
        dfs_val(next, node);
      }
    }
  };
  function<void(int, int, int)> dfs_add = [&] (int node, int par, int x) {
    if (x == 1) {
      at[val[node]].insert(dep[node]);
    } else if (x == -1) {
      assert(at[val[node]].count(dep[node]));
      at[val[node]].erase(at[val[node]].find(dep[node]));
    } else if (x == 2) {
      if (K - val[node] > 0 && at[K - val[node]].size()) {
        ans = min(ans, dep[node] + *at[K - val[node]].begin());
      }
    }
    for (auto [next, wt] : edges[node]) {
      if (next != par && !visited[next]) {
        dfs_add(next, node, x);
      }
    }
  };
  function<void(int, int)> dfs = [&] (int node, int par) {
    dfs_sz(node, par);
    int cent = centroid(node, par, sz[node]);
    visited[cent] = true;
    dep[cent] = val[cent] = 0;
    dfs_val(cent, -1);
    for (auto [next, wt] : edges[cent]) {
      if (!visited[next]) {
        dfs_add(next, cent, 1);
      }
    }
    for (auto [next, wt] : edges[cent]) {
      if (!visited[next]) {
        dfs_add(next, cent, -1);
        dfs_add(next, cent, 2);
        dfs_add(next, cent, 1);
      }
    }
    for (auto [next, wt] : edges[cent]) {
      if (!visited[next]) {
        dfs(next, cent);
      }
    }
  };
  dfs(0, -1);
  return (ans == 1e9 ? -1 : ans);
}

• Subtask 1: 0 / 9
• Subtask 2: 0 / 12
• Subtask 3: 0 / 22
• Subtask 4: 0 / 57