Maximum Trailing Zeros in a Cornered Path

Problem Description

You are given a 2D integer array grid of size m x n, where each cell contains a positive integer. A cornered path is defined as a set of adjacent cells with at most one turn. The product of a path is defined as the product of all the values in the path. Return the maximum number of trailing zeros in the product of a cornered path found in grid.

Key Insights

• A cornered path can either be purely horizontal, purely vertical, or consist of one turn from horizontal to vertical or vice versa.
• Trailing zeros in a number are determined by the number of pairs of factors 2 and 5 in its prime factorization, as 10 = 2 * 5.
• We can calculate the number of trailing zeros in the product of the path by counting the minimum of the count of 2s and 5s across the selected cells in the path.

Space and Time Complexity

Time Complexity: O(m * n)
Space Complexity: O(1)

Solution

To solve the problem, we will:

1. Iterate through each cell in the grid as a potential starting point for the path.
2. For each starting point, compute products for all possible horizontal and vertical paths, including paths that take one turn.
3. Count the number of factors 2 and 5 in the products of these paths to determine the number of trailing zeros.
4. Track the maximum number of trailing zeros found across all valid paths.

The algorithm primarily utilizes nested loops to explore the paths, and a simple counting mechanism to track the factors of 2 and 5.

Code Solutions