How should I practice DSA Round: Maximum Score Grid Path?

Start by reading the full statement, solve the visible examples, then compare the pattern against related OpenAI online assessment problems in FastPrep.

Is DSA Round: Maximum Score Grid Path associated with OpenAI?

FastPrep tags this as a OpenAI coding interview or online assessment practice problem when the problem catalog has that company context.

Problem · Dynamic Programming

DSA Round: Maximum Score Grid Path

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● HardOpenAIFULLTIMEONSITE INTERVIEW

Problem statement

You are given a rectangular grid board of size N x M, where each cell contains an integer. A player starts from cell (0, p) in the top row. The objective is to reach the bottom row of the grid while maximizing the total score collected.

From a cell (i, j), the player may move to:

(i + 1, j - 1), diagonally left-down
(i + 1, j), straight down
(i + 1, j + 1), diagonally right-down
(i + 2, j), using a special jump move

The player must always remain inside the grid boundaries. The special jump move (i + 2, j) may be used at most k times during the traversal.

The total score is equal to the sum of all visited cell values, including the starting cell and the final cell.

Complete the function maximizeGridPathScore. It should return a String[] with exactly three values:

result[0]: the maximum achievable score from the starting cell to any cell in the last row.
result[1]: one path that produces the maximum score, formatted as coordinates joined by ->, for example (0,1)->(1,1).
result[2]: the number of distinct maximum-score paths modulo 10^9 + 7.

If multiple maximum-score paths exist, return the lexicographically smallest coordinate sequence as the path in result[1]. Compare two paths by their coordinate pairs from left to right; the smaller row wins first, then the smaller column.

What the interview report shared

The source described an OpenAI onsite DSA round problem about maximizing score while moving through a rectangular integer grid. It listed the four allowed moves, including a limited special jump, and asked for the maximum score, one maximum-score path, and the count of maximum-score paths modulo 10^9 + 7.

How FastPrep adapted it

FastPrep kept the source task and example board, and added a deterministic return format so the problem can be practiced and checked here. The source asked for one valid maximum-score path but did not specify how to choose among ties, so FastPrep uses the lexicographically smallest maximum-score coordinate sequence for that returned path.

Function

maximizeGridPathScore(board: int[][], p: int, k: int) → String[]

Examples

Example 1

board = [[1,2,3,4],[5,6,1,2],[7,8,9,1],[3,2,5,6]]p = 1k = 1return = ["23","(0,1)->(1,1)->(2,2)->(3,3)","1"]

One maximum-score path is (0,1)->(1,1)->(2,2)->(3,3).

Visited values: 2 + 6 + 9 + 6 = 23.
The alternate valid jump path shown in the source, (0,1)->(2,1)->(3,2), scores 2 + 8 + 5 = 15, so it is not a maximum-score path.
There is exactly one maximum-score path for this example.

The source image provided valid path examples but did not state the final output values; these values follow directly from the source board and movement rules.

Constraints

board is rectangular and contains integers.
p is a valid column index in the top row.
The player may use the special jump at most k times.
Return the maximum-path count modulo 10^9 + 7.