Implement exponentiation and fill grid distances

You are given two separate coding tasks.

Task 1: Implement fast exponentiation

Implement a function pow(x, n) that returns $x^n$.

• Input :
  • x : a real number (double/float)
  • n : a 32-bit signed integer (can be negative)
• Output : the value $x^n$ as a floating-point number
• Requirements / edge cases :
  • Handle n < 0 (e.g., $x^{-n} = 1/x^n$ ).
  • n may be -2^31 , so be careful when negating.
  • Aim for $O(\log |n|)$ time.

Task 2: Fill shortest distance to a gate in a grid

You are given an m x n grid of integers representing a map:

• -1 represents a wall (blocked cell)
• 0 represents a gate
• A large sentinel value (e.g., INF = 2^31 - 1 ) represents an empty room

Update the grid in-place so that each empty room contains the distance (minimum number of moves) to its nearest gate.

• Moves are allowed only in 4 directions: up/down/left/right.
• If an empty room cannot reach any gate, it should remain INF .

Example

Input:

INF  -1   0  INF
INF INF INF  -1
INF  -1 INF  -1
0    -1 INF INF

Output:

3   -1  0   1
2    2  1  -1
1   -1  2  -1
0   -1  3   4

• Constraints (typical) :
  • 1 <= m, n <= 200 (or similar)
  • Grid updates must be done without changing wall/gate cells.