What is the time complexity of Count Cells in Overlapping Horizontal and Vertical Substrings?

The optimal solution for Count Cells in Overlapping Horizontal and Vertical Substrings runs in O(m * n) time and uses O(m * n) space. Efficiently checks for matches using rolling hash, minimizing redundant checks.

What is the brute force solution for Count Cells in Overlapping Horizontal and Vertical Substrings?

The brute force approach for Count Cells in Overlapping Horizontal and Vertical Substrings is Brute Force, with O(m * n * (m + n)) time complexity and O(m * n) space complexity. Check every possible starting position for horizontal and vertical substrings. This method is straightforward but inefficient for larger grids. The optimal Optimal Solution approach improves this to O(m * n).

What algorithm or data structure is used to solve Count Cells in Overlapping Horizontal and Vertical Substrings?

Count Cells in Overlapping Horizontal and Vertical Substrings uses the following concepts: Array, String, Rolling Hash, String Matching, Matrix, Hash Function. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Count Cells in Overlapping Horizontal and Vertical Substrings?

Clarify the problem constraints. Discuss potential optimizations early. Practice similar pattern matching problems.

What are common mistakes when solving Count Cells in Overlapping Horizontal and Vertical Substrings?

Not accounting for wrapping correctly. Overlooking edge cases with small grids.

#3529

Count Cells in Overlapping Horizontal and Vertical Substrings

Medium

ArrayStringRolling HashString MatchingMatrixHash FunctionHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

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

Utilize rolling hash to efficiently find occurrences of the pattern both horizontally and vertically, reducing unnecessary checks.

⚙️

Algorithm

3 steps

1Step 1: Create a rolling hash function to find horizontal occurrences of the pattern.
2Step 2: Store the positions of horizontal matches in a set.
3Step 3: Create a similar rolling hash for vertical occurrences and count overlapping positions.

solution.py15 lines

1def count_cells(grid, pattern):
2    m, n = len(grid), len(grid[0])
3    horizontal_positions = set()
4    pattern_len = len(pattern)
5    for i in range(m):
6        for j in range(n):
7            if j + pattern_len <= n and ''.join(grid[i][j:j+pattern_len]) == pattern:
8                horizontal_positions.update((i, j+k) for k in range(pattern_len))
9    count = 0
10    for j in range(n):
11        for i in range(m):
12            if i + pattern_len <= m:
13                if ''.join(grid[i+k][j] for k in range(pattern_len)) == pattern:
14                    count += sum((1 for k in range(pattern_len) if (i+k, j) in horizontal_positions))
15    return count

ℹ

Complexity note: Efficiently checks for matches using rolling hash, minimizing redundant checks.

1Horizontal and vertical checks are independent but must intersect.
2Using sets allows for efficient overlap checks.

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