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675. Cut Off Trees for Golf Event

  • Time: $O(m^2n^2)$
  • Space: $O(mn)$
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struct T {
  int i;
  int j;
  int height;
};

class Solution {
 public:
  int cutOffTree(vector<vector<int>>& forest) {
    auto compare = [&](const T& a, const T& b) { return a.height > b.height; };
    priority_queue<T, vector<T>, decltype(compare)> minHeap(compare);

    for (int i = 0; i < forest.size(); ++i)
      for (int j = 0; j < forest[0].size(); ++j)
        if (forest[i][j] > 1)
          minHeap.emplace(i, j, forest[i][j]);

    int ans = 0;
    int x = 0;
    int y = 0;

    while (!minHeap.empty()) {
      const auto [i, j, _] = minHeap.top();
      minHeap.pop();
      // Walk from (x, y) to (i, j).
      const int step = bfs(forest, x, y, i, j);
      if (step < 0)
        return -1;
      ans += step;
      x = i;
      y = j;
    }

    return ans;
  }

 private:
  static constexpr int dirs[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};

  int bfs(const vector<vector<int>>& forest, int si, int sj, int ei, int ej) {
    const int m = forest.size();
    const int n = forest[0].size();
    queue<pair<int, int>> q{{{si, sj}}};
    vector<vector<bool>> seen(m, vector<bool>(n));
    seen[si][sj] = true;

    for (int step = 0; !q.empty(); ++step)
      for (int sz = q.size(); sz > 0; --sz) {
        const auto [i, j] = q.front();
        q.pop();
        if (i == ei && j == ej)
          return step;
        for (const auto& [dx, dy] : dirs) {
          const int x = i + dx;
          const int y = j + dy;
          if (x < 0 || x == m || y < 0 || y == n)
            continue;
          if (seen[x][y] || forest[x][y] == 0)
            continue;
          q.emplace(x, y);
          seen[x][y] = true;
        }
      }

    return -1;
  };
};

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class T {
  public int i;
  public int j;
  public int height;
  public T(int i, int j, int height) {
    this.i = i;
    this.j = j;
    this.height = height;
  }
}

class Solution {
  public int cutOffTree(List<List<Integer>> forest) {
    Queue<T> minHeap = new PriorityQueue<>((a, b) -> Integer.compare(a.height, b.height));

    for (int i = 0; i < forest.size(); ++i)
      for (int j = 0; j < forest.get(0).size(); ++j)
        if (forest.get(i).get(j) > 1)
          minHeap.offer(new T(i, j, forest.get(i).get(j)));

    int ans = 0;
    int x = 0;
    int y = 0;

    while (!minHeap.isEmpty()) {
      final int i = minHeap.peek().i;
      final int j = minHeap.poll().j;
      // Walk from (x, y) to (i, j).
      final int step = bfs(forest, x, y, i, j);
      if (step < 0)
        return -1;
      ans += step;
      x = i;
      y = j;
    }

    return ans;
  }

  private static final int[][] dirs = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};

  private int bfs(List<List<Integer>> forest, int si, int sj, int ei, int ej) {
    final int m = forest.size();
    final int n = forest.get(0).size();
    Queue<Pair<Integer, Integer>> q = new ArrayDeque<>(List.of(new Pair<>(si, sj)));
    boolean[][] seen = new boolean[m][n];
    seen[si][sj] = true;

    for (int step = 0; !q.isEmpty(); ++step)
      for (int sz = q.size(); sz > 0; --sz) {
        final int i = q.peek().getKey();
        final int j = q.poll().getValue();
        if (i == ei && j == ej)
          return step;
        for (int[] dir : dirs) {
          final int x = i + dir[0];
          final int y = j + dir[1];
          if (x < 0 || x == m || y < 0 || y == n)
            continue;
          if (seen[x][y] || forest.get(x).get(y) == 0)
            continue;
          q.offer(new Pair<>(x, y));
          seen[x][y] = true;
        }
      }

    return -1;
  };
}