Longest Increasing Path

Problem Statement:

Given an m x n integer matrix, write a function to find the length of the longest increasing path in the matrix. From each cell, you can move in four directions: left, right, up, or down. You may not move diagonally or move outside the boundary of the matrix. You may only move to a cell with a strictly greater value than the current cell.

Requirements:

• Implement a function which takes a 2D array of integers as input and returns an integer representing the length of the longest increasing path.
• Optimize your solution for time complexity.
• Consider edge cases such as empty matrices or when no increasing path exists.

Input/Output Example:

For example, given the matrix:

[
  [9, 9, 4],
  [6, 6, 8],
  [2, 1, 1]
]

The longest increasing path is [1, 2, 6, 9] (or any other valid path with the same values ordered increasingly), so the function should return 4.

Note:

• Only provide the code solution without any extra explanation or development commentary.
• Assume any necessary helper functions or standard libraries are allowed depending on your programming language of choice.

Good luck!