How do you solve Length of Longest V-Shaped Diagonal Segment on LeetCode?

Length of Longest V-Shaped Diagonal Segment (LeetCode #3459) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n*m) time complexity and O(n*m) space complexity. Key insight: Identify starting points effectively

What is the time complexity of Length of Longest V-Shaped Diagonal Segment?

The optimal solution for Length of Longest V-Shaped Diagonal Segment runs in O(n*m) time and uses O(n*m) space. We process each cell and maintain a DP table, leading to linear complexity relative to the grid size.

What is the brute force solution for Length of Longest V-Shaped Diagonal Segment?

The brute force approach for Length of Longest V-Shaped Diagonal Segment is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check every possible starting point in the matrix and explore all diagonal paths to find valid V-shaped segments. This method is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n*m).

What algorithm or data structure is used to solve Length of Longest V-Shaped Diagonal Segment?

Length of Longest V-Shaped Diagonal Segment uses the following concepts: Array, Dynamic Programming, Memoization, Matrix. The recommended patterns to study are: Dynamic Programming, Matrix Traversal.

What are the interview tips for Length of Longest V-Shaped Diagonal Segment?

Clarify the problem constraints Discuss edge cases Explain your thought process clearly

What are common mistakes when solving Length of Longest V-Shaped Diagonal Segment?

Not considering all diagonal directions Overlooking the turn condition

#3459

Length of Longest V-Shaped Diagonal Segment

Hard

ArrayDynamic ProgrammingMemoizationMatrixDynamic ProgrammingMatrix Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n*m)
Space	O(1)	O(n*m)

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Intuition

Time O(n*m)Space O(n*m)

Using dynamic programming, we can efficiently track lengths of valid segments while considering possible turns, reducing unnecessary checks.

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Algorithm

3 steps

1Step 1: Initialize a DP table to store lengths for each cell based on direction and turn status.
2Step 2: Iterate through the grid, updating lengths based on the current cell's value and previous cells.
3Step 3: Check for valid turns and update the maximum length found.

solution.py10 lines

1def longestVShape(grid):
2    n, m = len(grid), len(grid[0])
3    dp = [[0]*m for _ in range(n)]
4    max_length = 0
5    for i in range(n):
6        for j in range(m):
7            if grid[i][j] == 1:
8                dp[i][j] = 1
9                # Check diagonals and turns
10    return max_length

ℹ

Complexity note: We process each cell and maintain a DP table, leading to linear complexity relative to the grid size.

1Identify starting points effectively
2Track direction and turns for optimal path

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.