Unique Grid Path Combinations | Dataford Interview Questions

A Wealthfront interface models a navigation flow as an n x m grid. Starting at the top-left cell, a user may move only one cell right or one cell down. Return the total number of distinct paths to the bottom-right cell.

The result must be exact. Do not construct the full grid or use a recursive solution that recomputes the same states.

Formal Specification

Implement unique_paths(rows, cols), where rows and cols are positive integers. Return an integer equal to the number of valid paths from (0, 0) to (rows - 1, cols - 1).

A valid path contains exactly rows - 1 down moves and cols - 1 right moves. Since the answer can be very large, use Python's arbitrary-precision integers.

Constraints

1 <= rows, cols <= 100000
rows and cols are integers
The exact result must be returned
Additional space must be less than O(rows * cols)

Function Signature

def unique_paths(rows, cols):

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