How do you solve Diagonal Traverse on LeetCode?

Diagonal Traverse (LeetCode #498) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding the pattern of diagonal traversal helps in optimizing the solution.

What is the brute force solution for Diagonal Traverse?

The brute force approach for Diagonal Traverse is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves iterating through each element of the matrix and collecting them in a diagonal order. We can achieve this by simulating the diagonal traversal using nested loops. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Diagonal Traverse?

Diagonal Traverse uses the following concepts: Array, Matrix, Simulation. The recommended patterns to study are: Array, Matrix.

What are the interview tips for Diagonal Traverse?

Always clarify the problem statement and constraints before jumping into coding. Think aloud while solving to demonstrate your thought process. Consider edge cases and test your solution with them.

What are common mistakes when solving Diagonal Traverse?

Failing to handle edge cases like empty matrices. Not correctly determining the boundaries of the matrix during traversal.

#498

Diagonal Traverse

Medium

ArrayMatrixSimulationArrayMatrix

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

The optimal solution leverages the understanding of how diagonals are formed in the matrix and uses a single loop to traverse through the diagonals efficiently, reducing unnecessary checks.

⚙️

Algorithm

3 steps

1Step 1: Initialize an empty list to store the result.
2Step 2: Use a single loop to iterate through the sum of indices (d) from 0 to m + n - 2.
3Step 3: Depending on whether d is even or odd, determine the starting point and direction of traversal, collecting elements along the diagonal.

solution.py23 lines

1# Full working Python code
2
3def findDiagonalOrder(mat):
4    if not mat:
5        return []
6    m, n = len(mat), len(mat[0])
7    result = []
8    for d in range(m + n - 1):
9        if d % 2 == 0:
10            row = min(d, m - 1)
11            col = d - row
12            while row >= 0 and col < n:
13                result.append(mat[row][col])
14                row -= 1
15                col += 1
16        else:
17            col = min(d, n - 1)
18            row = d - col
19            while col >= 0 and row < m:
20                result.append(mat[row][col])
21                row += 1
22                col -= 1
23    return result

ℹ

Complexity note: The time complexity is O(n) because we traverse each element of the matrix once. The space complexity is O(n) for storing the result array.

1Understanding the pattern of diagonal traversal helps in optimizing the solution.
2Recognizing the direction of traversal (up or down) based on the sum of indices is crucial.

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