Is Minimum Cost Path with Alternating Directions I easy or hard?

The problem is rated Medium because the main difficulty lies in recognizing the constraint that drastically reduces the number of possible paths. Once you identify that only two alternating patterns exist, the implementation becomes straightforward and runs in linear time.

Minimum Cost Path with Alternating Directions I Python/Java solution

The implementation simulates two candidate paths: one starting with the first direction and the other with the opposite direction. For each step, alternate the direction and accumulate the grid cost until the destination is reached. This logic translates directly into Python, Java, C++, Go, or TypeScript with a simple loop.

How to solve Minimum Cost Path with Alternating Directions I in O(n)?

Recognize that strict alternation eliminates most possible paths. Only two sequences exist: one starting with the first direction and the other starting with the second. Simulate both paths, accumulate the cost of visited cells, and return the minimum valid result. This converts the problem from path search to simple linear simulation.

What is the best approach for Minimum Cost Path with Alternating Directions I?

The optimal approach evaluates the two possible alternating direction patterns. Since moves must alternate, once the starting direction is chosen the entire path sequence becomes fixed. Compute the total cost for both valid patterns and return the minimum. This runs in O(n) time with O(1) extra space.

Is Minimum Cost Path with Alternating Directions I asked at Google/Amazon/Meta?

Problems involving constrained grid paths and pattern-based reasoning appear frequently in interviews at companies like Google, Amazon, and Meta. While the exact question may vary, the underlying idea of reducing a search space using mathematical observation is a common interview theme.

What data structure is used in Minimum Cost Path with Alternating Directions I?

No complex data structure is required for the optimal solution. The algorithm relies on simple iteration and integer variables to track the current position and cumulative cost. The key insight is mathematical reasoning about the limited number of valid paths.

What is the time complexity of Minimum Cost Path with Alternating Directions I?

The optimal solution runs in O(n) time where n represents the number of steps in the path. Only two deterministic paths are evaluated, so the algorithm simply iterates along each path once. Space complexity remains O(1) because no additional data structures are required.

3596. Minimum Cost Path with Alternating Directions I - Practice Online

You are given two integers m and n representing the number of rows and columns of a grid, respectively.

The cost to enter cell (i, j) is defined as (i + 1) * (j + 1).

The path will always begin by entering cell (0, 0) on move 1 and paying the entrance cost.

At each step, you move to an adjacent cell, following an alternating pattern:

On odd-numbered moves, you must move either right or down.
On even-numbered moves, you must move either left or up.

Return the minimum total cost required to reach (m - 1, n - 1). If it is impossible, return -1.

Example 1:

Input: m = 1, n = 1

Output: 1

Explanation:

You start at cell (0, 0).
The cost to enter (0, 0) is (0 + 1) * (0 + 1) = 1.
Since you're at the destination, the total cost is 1.

Example 2:

Input: m = 2, n = 1

Output: 3

Explanation:

You start at cell (0, 0) with cost (0 + 1) * (0 + 1) = 1.
Move 1 (odd): You can move down to (1, 0) with cost (1 + 1) * (0 + 1) = 2.
Thus, the total cost is 1 + 2 = 3.

Constraints:

1 <= m, n <= 10⁶