Submission #961449

#	Time	Username	Problem	Language	Result	Execution time	Memory
961449		kilkuwu	Swapping Cities (APIO20_swap)	C++17	100 / 100	306 ms	41688 KiB

swap

#include "swap.h"

#include <bits/stdc++.h>

template <typename T>
inline bool ckmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}

template <typename T>
inline bool ckmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}

constexpr int mxM = 200'000;
constexpr int mxN = 100'000;
constexpr int LOG = 20;
constexpr int inf = 1e9 + 7;

struct Edge {
  int u, v, w;

  bool operator<(const Edge& rhs) const {
    return w < rhs.w;
  }

  inline int other(int x) { return u ^ v ^ x; }
};

Edge edges[mxM];
std::vector<std::pair<int, int>> adj[mxN];

int up[LOG][mxN];
int vv[LOG][mxN];
int dep[mxN];

int num_nodes;

std::pair<int, int> par[mxN + mxM];

std::pair<int, int> find(int u) {
  if (par[u].first == -1) {
    return {u, par[u].second};
  }

  auto pu = find(par[u].first);
  pu.second = std::min(pu.second, par[u].second);

  return par[u] = pu;
}

void merge(int u, int v, int w) {

  auto pu = find(u), pv = find(v);

  par[pu.first].first = par[pv.first].first = num_nodes;

  if (par[pu.first].second <= 1e9) {
    ckmin(par[num_nodes].second, w);
  }

  if (par[pv.first].second <= 1e9) {
    ckmin(par[num_nodes].second, w);
  }

  if (pu.first == pv.first) {
    ckmin(par[num_nodes].second, w);
  } else {
    adj[u].emplace_back(w, v);
    adj[v].emplace_back(w, u);
  }

  if (adj[u].size() > 2 || adj[v].size() > 2) {
    ckmin(par[num_nodes].second, w);
  }

  //std::cerr << u << " " << v << " " << w << " " << par[num_nodes].second << std::endl;
  num_nodes++;
}

void dfs(int u) {
  for (auto [w, v] : adj[u]) {
    if (v == up[0][u]) continue;
    dep[v] = dep[u] + 1;
    up[0][v] = u;
    vv[0][v] = w;
    dfs(v);
  } 
}

void init(int N, int M,
          std::vector<int> U, std::vector<int> V, std::vector<int> W) {
  
  for (int i = 0; i < N + M; i++) {
    par[i] = {-1, inf};
  }

  num_nodes = N;
  for (int i = 0; i < M; i++) {
    edges[i] = {U[i], V[i], W[i]};
  }

  std::sort(edges, edges + M);

  for (int i = 0; i < M; i++) {
    auto [u, v, w] = edges[i];
    merge(u, v, w);
  }

  dfs(0);

  for (int k = 0; k + 1 < LOG; k++) {
    for (int i = 0; i < N; i++) {
      up[k + 1][i] = up[k][up[k][i]];
      vv[k + 1][i] = std::max(vv[k][i], vv[k][up[k][i]]);
    }
  }
}

int max_path(int u, int v) {
  if (dep[u] > dep[v]) std::swap(u, v);
  int d = dep[v] - dep[u];
  int ans = 0;
  for (int k = 0; k < LOG; k++) {
    if (d >> k & 1) {
      ckmax(ans, vv[k][v]);
      v = up[k][v];
    }
  }

  if (u == v) return ans;

  for (int k = LOG - 1; k >= 0; k--) {
    if (up[k][u] != up[k][v]) {
      ckmax(ans, vv[k][u]);
      ckmax(ans, vv[k][v]);
      u = up[k][u];
      v = up[k][v];
    }
  }

  ckmax(ans, vv[0][u]);
  ckmax(ans, vv[0][v]);

  return ans;
}

int getMinimumFuelCapacity(int X, int Y) {
  int ans = std::min(find(X).second, find(Y).second);
  ans = std::max(ans, max_path(X, Y));
  return ans <= 1e9 ? ans : -1; 
}

/*

8 7
2 0 9
2 1 3
1 3 1
0 5 6
5 4 5
1 6 3
3 7 4
1 
0 4 


*/

• Subtask 1: 6 / 6
• Subtask 2: 7 / 7
• Subtask 3: 17 / 17
• Subtask 4: 20 / 20
• Subtask 5: 23 / 23
• Subtask 6: 27 / 27