Python Coding challenge - Day 536| What is the output of the following Python Code?

 

Code Explanation:

1. Import LRU Cache Decorator

from functools import lru_cache

Imports the lru_cache decorator from Python’s functools module.

lru_cache is used to memoize function results — it remembers function calls with specific arguments and caches the return value, so repeated calls are fast.

2. Define the Function with Memoization

@lru_cache(None)

def unique_paths(m, n):

@lru_cache(None) tells Python to cache unlimited previous calls of unique_paths(m, n).

unique_paths(m, n) returns the number of unique paths in an m x n grid (from top-left to bottom-right, only moving right or down).

3. Base Case

    if m == 1 or n == 1:

        return 1

If either m == 1 (only one row) or n == 1 (only one column), there’s only one possible path — go straight down or right.

This is the base case for the recursion.

4. Recursive Case

    return unique_paths(m - 1, n) + unique_paths(m, n - 1)

If you're not at the base case, you can:

Move down: unique_paths(m - 1, n)

Move right: unique_paths(m, n - 1)

So, total paths = sum of those two possibilities.

This forms a top-down recursive solution with memoization to prevent repeated work.

5. Call and Print the Result

print(unique_paths(3, 7))

Calculates the number of unique paths in a 3 x 7 grid.

Output: 28

(There are 28 different paths from the top-left to the bottom-right in such a grid.)

Final Output:

28

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