結果

問題 No.2855 Move on Grid
ユーザー Daniel KDaniel K
提出日時 2024-08-25 16:11:16
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,043 ms / 3,000 ms
コード長 5,235 bytes
コンパイル時間 1,890 ms
コンパイル使用メモリ 141,964 KB
実行使用メモリ 16,600 KB
最終ジャッジ日時 2024-08-25 16:11:50
合計ジャッジ時間 33,036 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
other AC * 40
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <list>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <cmath>
#include <utility>
#include <sstream>
#include <queue>
#include <queue>

using namespace std;

vector<int> parent;
vector<int> rrank;
vector<vector<int>> adj_list;
vector<int> distances;

using weighted_key = tuple<int, int>;
unordered_set<int> visited;
priority_queue<weighted_key, vector<weighted_key>, std::greater<>> pqueue;

int find_set(int v) {
  if (v == parent[v])
    return v;
  return parent[v] = find_set(parent[v]);
}

void make_set(int v) {
  parent[v] = v;
  rrank[v] = 0;
}

void union_sets(int a, int b) {
  a = find_set(a);
  b = find_set(b);
  if (a != b) {
    if (rrank[a] < rrank[b])
      swap(a, b);
    parent[b] = a;
    if (rrank[a] == rrank[b])
      rrank[a]++;
  }
}

bool solve(const vector<vector<int>> &grid, const int k, const int desired_minimum) {
  int n = grid.size();
  int m = grid[0].size();
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      make_set(i * m + j);
    }
  }

  vector<pair<int, int>> dirs = {{{-1, 0}, {1, 0}, {0, 1}, {0, -1}}};
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      if (grid[i][j] < desired_minimum) {
        continue;
      }
      int key = i * m + j;

      for (const auto &d: dirs) {
        int nexti = i + d.first;
        int nextj = j + d.second;
        if (nexti < 0 || nextj < 0 || nexti >= n || nextj >= m) {
          continue;
        }
        if (grid[nexti][nextj] < desired_minimum) {
          continue;
        }

        int nextkey = nexti * m + nextj;
        union_sets(key, nextkey);
      }
    }
  }

  //  cerr << "components: ";
  //  for (int i = 0; i < n; ++i) {
  //    for (int j = 0; j < m; ++j) {
  //      cerr << "(" << i << "," << j << "): " << find_set(i * m + j) << ", ";
  //    }
  //  }
  //  cerr << endl;

  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      adj_list[i * m + j].clear();
    }
  }

  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      int pcur = find_set(i * m + j);

      for (const auto &d: dirs) {
        int nexti = i + d.first;
        int nextj = j + d.second;
        if (nexti < 0 || nextj < 0 || nexti >= n || nextj >= m) {
          continue;
        }

        int pnext = find_set(nexti * m + nextj);

        if (pnext == pcur) {
          continue;
        }

        adj_list[pcur].emplace_back(pnext);
        adj_list[pnext].emplace_back(pcur);
      }
    }
  }

  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      auto &arr = adj_list[i * m + j];
      std::sort(arr.begin(), arr.end());
      auto last = std::unique(arr.begin(), arr.end());
      arr.erase(last, arr.end());
    }
  }

  // find dist from (0,0) to (n-1, m-1)

  visited.clear();
  while (!pqueue.empty()) {
    pqueue.pop();
  }

  int start_weight = 0;
  if (grid[0][0] < desired_minimum) {
    start_weight = 1;
  }
  std::fill(distances.begin(), distances.end(), -1);
  distances[find_set(0)] = start_weight;
  pqueue.emplace(start_weight, find_set(0));
  int target = find_set(n * m - 1);
  while (!pqueue.empty()) {
    int cur_dist = std::get<0>(pqueue.top());
    int cur = std::get<1>(pqueue.top());
    pqueue.pop();
    if (visited.find(cur) != visited.end()) {
      continue;
    }
    visited.emplace(cur);

    if (cur == target) {
      break;
    }

    for (const auto &next: adj_list[cur]) {
      if (visited.find(next) != visited.end()) {
        continue;
      }
      //cerr << "from " << cur << " can reach " << next << endl;
      int next_r = next / m;
      int next_c = next % m;
      int next_cost = 0;
      if (grid[next_r][next_c] < desired_minimum) {
        next_cost += 1;
      }
      int next_dist = cur_dist + next_cost;
      if (distances[next] == -1 || distances[next] > next_dist) {
        distances[next] = next_dist;
        pqueue.emplace(next_dist, next);
      }
    }
  }

  int dist_to_goal = distances[target];
  //  cerr << "num steps to go from (0,0) (comp=" << find_set(0) << ") to (n-1,m-1) (comp=" << target << "): "
  //       << dist_to_goal << endl;
  bool solvable = dist_to_goal <= k;
  return solvable;
}

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

  int64_t n, m, k;
  cin >> n >> m >> k;
  vector<vector<int>> grid(n, vector<int>(m));
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      cin >> grid[i][j];
    }
  }
  parent.resize(n * m);
  rrank.resize(n * m);
  adj_list.resize(n * m);
  distances.resize(n * m);

  int lo_ans = 0;
  int hi_ans = 1000000001;
  while (lo_ans + 1 < hi_ans) {
    int mid_ans = lo_ans / 2 + hi_ans / 2 + ((lo_ans % 2) + (hi_ans % 2)) / 2;
    bool solvable = solve(grid, k, mid_ans);
//    cerr << "Is it solvable at ans=" << mid_ans << "? " << (solvable ? " yes " : " no ") << "(lo=" << lo_ans << ", hi="
//         << hi_ans << ")" << endl;

    if (solvable) {
      // this could be the solution, don't rule it out.
      lo_ans = mid_ans;
    } else {
      // ans must be less than mid_ans
      hi_ans = mid_ans;
    }

  }

  cout << lo_ans << endl;

  return 0;
}
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