Painting the Walls — LeetCode 2742 Python Solution

The problem

You are given two 0-indexed integer arrays, cost and time, of size n representing the costs and the time taken to paint n different walls respectively. There are two painters available: A paid painter that paints the ith wall in time[i] units of time and takes cost[i] units of money.

Example

Input

cost = [1,2,3,2], time = [1,2,3,2]

Output

3

Explanation

The walls at index 0 and 1 will be painted by the paid painter, and it will take 3 units of time; meanwhile, the free painter will paint the walls at index 2 and 3, free of cost in 2 units of time. Thus, the total cost is 1 + 2 = 3.

Python solution

class Solution:
    def paintWalls(self, cost: List[int], time: List[int]) -> int:
        @cache
        def dfs(i: int, j: int) -> int:
            if n - i <= j:
                return 0
            if i >= n:
                return inf
            return min(dfs(i + 1, j + time[i]) + cost[i], dfs(i + 1, j - 1))

        n = len(cost)
        return dfs(0, 0)

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2742. Painting the Walls is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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