Walls and Gates

You are given a 2D grid, rooms, made up of m rows and n columns, representing the floor plan of a building. Each cell holds one of three possible values:

• -1 — a wall or an obstacle that cannot be passed through.
• 0 — a gate.
• 2147483647 (i.e. INT_MAX) — an empty room.

Starting from every empty room, you may move up, down, left, or right into an adjacent cell, but never diagonally, and never through a wall. Fill each empty room in the grid with the length of the shortest path from that room to its nearest gate. If a room cannot reach any gate at all, it should keep the value 2147483647.

Modify the grid in place — the function does not need to return anything, but the grid passed in should end up holding the final distances.

• There can be more than one gate on the grid, and a room only needs the distance to the closest one.
• Distance is measured in the number of moves between adjacent cells, not straight-line distance.
• Walls block movement entirely; you cannot pass through them or land on them.

Examples

Example 1:

Input: rooms = [[2147483647,-1,0],[2147483647,2147483647,2147483647],[2147483647,-1,2147483647]]

Output: [[3,-1,0],[2,2,1],[1,-1,2]]

Explanation:

• The grid is 3 rows by 3 columns, with a single gate at position (0,2).
• The wall at (0,1) and the wall at (2,1) stay as -1 and are never overwritten.
• The room at (1,2) is directly above... actually adjacent to the gate, so it becomes 1; the room at (2,2) is two steps away, so it becomes 2.
• The room at (0,0) must travel around the wall at (0,1), taking a path of length 3 through (1,0) -> (1,1) -> (1,2) -> (0,2).

Example 2:

Input: rooms = [[0,-1],[2147483647,2147483647]]

Output: [[0,-1],[1,2]]

Explanation:

• The single gate sits at (0,0).
• The cell at (1,0) is adjacent to the gate, giving distance 1.
• The cell at (1,1) cannot reach the gate directly (its neighbor (0,1) is a wall), so it must route through (1,0), giving distance 2.

Example 3:

Input: rooms = [[2147483647]]

Output: [[2147483647]]

Explanation:

• There are no gates anywhere on the grid, so the single empty room has no path to any gate and keeps its original placeholder value.

Constraints

• m == rooms.length
• n == rooms[i].length
• 1 <= m, n <= 250
• rooms[i][j] is one of -1, 0, or 2147483647.