length-of-longest-v-shaped-diagonal-segment

You are given a 2D integer matrix grid of size n x m, where each element is either 0, 1, or 2.

A V-shaped diagonal segment is defined as:

• The segment starts with 1.


• The subsequent elements follow this infinite sequence: 2, 0, 2, 0, ....


• The segment:
  
  
  
  • Starts along a diagonal direction (top-left to bottom-right, bottom-right to top-left, top-right to bottom-left, or bottom-left to top-right).
  
  
  • Continues the sequence in the same diagonal direction.
  
  
  • Makes at most one clockwise 90-degree turn to another diagonal direction while maintaining the sequence.
  
  
  
  

Return the length of the longest V-shaped diagonal segment. If no valid segment exists, return 0.

Example 1:

Input: grid = [[2,2,1,2,2],[2,0,2,2,0],[2,0,1,1,0],[1,0,2,2,2],[2,0,0,2,2]]

Output: 5

Explanation:

The longest V-shaped diagonal segment has a length of 5 and follows these coordinates: (0,2) → (1,3) → (2,4), takes a 90-degree clockwise turn at (2,4), and continues as (3,3) → (4,2).

Example 2:

Input: grid = [[2,2,2,2,2],[2,0,2,2,0],[2,0,1,1,0],[1,0,2,2,2],[2,0,0,2,2]]

Output: 4

Explanation:

The longest V-shaped diagonal segment has a length of 4 and follows these coordinates: (2,3) → (3,2), takes a 90-degree clockwise turn at (3,2), and continues as (2,1) → (1,0).

Example 3:

Input: grid = [[1,2,2,2,2],[2,2,2,2,0],[2,0,0,0,0],[0,0,2,2,2],[2,0,0,2,0]]

Output: 5

Explanation:

The longest V-shaped diagonal segment has a length of 5 and follows these coordinates: (0,0) → (1,1) → (2,2) → (3,3) → (4,4).

Example 4:

Input: grid = [[1]]

Output: 1

Explanation:

The longest V-shaped diagonal segment has a length of 1 and follows these coordinates: (0,0).

Constraints:

• n == grid.length


• m == grid[i].length


• 1 <= n, m <= 500


• grid[i][j] is either 0, 1 or 2.