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542. 01 Matrix 👍

Approach 1: w/ boolean array

  • Time: $O(mn)$
  • Space: $O(mn)$
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class Solution {
 public:
  vector<vector<int>> updateMatrix(vector<vector<int>>& mat) {
    constexpr int dirs[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
    const int m = mat.size();
    const int n = mat[0].size();
    queue<pair<int, int>> q;
    vector<vector<bool>> seen(m, vector<bool>(n));

    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        if (mat[i][j] == 0) {
          q.emplace(i, j);
          seen[i][j] = true;
        }

    while (!q.empty()) {
      const auto [i, j] = q.front();
      q.pop();
      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])
          continue;
        mat[x][y] = mat[i][j] + 1;
        q.emplace(x, y);
        seen[x][y] = true;
      }
    }

    return mat;
  }
};

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class Solution {
  public int[][] updateMatrix(int[][] mat) {
    final int[][] dirs = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
    final int m = mat.length;
    final int n = mat[0].length;
    Queue<Pair<Integer, Integer>> q = new ArrayDeque<>();
    boolean[][] seen = new boolean[m][n];

    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        if (mat[i][j] == 0) {
          q.offer(new Pair<>(i, j));
          seen[i][j] = true;
        }

    while (!q.isEmpty()) {
      final int i = q.peek().getKey();
      final int j = q.poll().getValue();
      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])
          continue;
        mat[x][y] = mat[i][j] + 1;
        q.offer(new Pair<>(x, y));
        seen[x][y] = true;
      }
    }

    return mat;
  }
}

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class Solution:
  def updateMatrix(self, mat: list[list[int]]) -> list[list[int]]:
    dirs = ((0, 1), (1, 0), (0, -1), (-1, 0))
    m = len(mat)
    n = len(mat[0])
    q = collections.deque()
    seen = [[False] * n for _ in range(m)]

    for i in range(m):
      for j in range(n):
        if mat[i][j] == 0:
          q.append((i, j))
          seen[i][j] = True

    while q:
      i, j = q.popleft()
      for dx, dy in dirs:
        x = i + dx
        y = j + dy
        if x < 0 or x == m or y < 0 or y == n:
          continue
        if seen[x][y]:
          continue
        mat[x][y] = mat[i][j] + 1
        q.append((x, y))
        seen[x][y] = True

    return mat

Approach 2: w/o boolean array

  • Time: $O(mn)$
  • Space: $O(mn)$
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class Solution {
 public:
  vector<vector<int>> updateMatrix(vector<vector<int>>& mat) {
    constexpr int dirs[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
    const int m = mat.size();
    const int n = mat[0].size();
    queue<pair<int, int>> q;

    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        if (mat[i][j] == 0)
          q.emplace(i, j);
        else
          mat[i][j] = INT_MAX;

    while (!q.empty()) {
      const auto [i, j] = q.front();
      q.pop();
      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 (mat[x][y] <= mat[i][j] + 1)
          continue;
        q.emplace(x, y);
        mat[x][y] = mat[i][j] + 1;
      }
    }

    return mat;
  }
};

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class Solution {
  public int[][] updateMatrix(int[][] mat) {
    final int[][] dirs = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
    final int m = mat.length;
    final int n = mat[0].length;
    Queue<Pair<Integer, Integer>> q = new ArrayDeque<>();

    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        if (mat[i][j] == 0)
          q.offer(new Pair<>(i, j));
        else
          mat[i][j] = Integer.MAX_VALUE;

    while (!q.isEmpty()) {
      final int i = q.peek().getKey();
      final int j = q.poll().getValue();
      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 (mat[x][y] <= mat[i][j] + 1)
          continue;
        q.offer(new Pair<>(x, y));
        mat[x][y] = mat[i][j] + 1;
      }
    }

    return mat;
  }
}

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class Solution:
  def updateMatrix(self, mat: list[list[int]]) -> list[list[int]]:
    dirs = ((0, 1), (1, 0), (0, -1), (-1, 0))
    m = len(mat)
    n = len(mat[0])
    q = collections.deque()

    for i in range(m):
      for j in range(n):
        if mat[i][j] == 0:
          q.append((i, j))
        else:
          mat[i][j] = math.inf

    while q:
      i, j = q.popleft()
      for dx, dy in dirs:
        x = i + dx
        y = j + dy
        if x < 0 or x == m or y < 0 or y == n:
          continue
        if mat[x][y] <= mat[i][j] + 1:
          continue
        q.append((x, y))
        mat[x][y] = mat[i][j] + 1

    return mat