01 Matrix
Medium · Graphs · Explanation and code example
Multi-Source Breadth-First Search
How it works
Start BFS from every zero simultaneously. Every step from this frontier adds one to the nearest-zero distance, so the first visit to a cell gives its minimum distance. Store distances in the matrix while a separate seen grid prevents repeat visits.
Steps
- Enqueue all zeros and mark them seen.
- Visit unvisited orthogonal neighbors at parent distance + 1.
- Mark when enqueueing and return the updated matrix.
Complexity
- Time: O(rows × columns).
- Space: O(rows × columns).
Things to watch for
- Start from all zeros, rather than one zero.
- Only orthogonal moves count.
- This implementation overwrites the input matrix with distances.
Python code example
import collections
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
C++ code example
class Solution {
public:
vector<vector<int>> updateMatrix(vector<vector<int>>& mat) {
constexpr int kDirs[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] : kDirs) {
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;
}
};
Source and license
Explanation by LC Tracker. Code adapted from walkccc / Peng-Yu Chen · MIT license. Node types are supplied by LeetCode where needed.