Cross the most walls on a number line with limited energy

Walls stand at distinct non-zero integer points on an infinite number line. Wall k is at positions[k] and costs costs[k] >= 0 energy to cross.

You start at 0 with energy units. Each step moves you one unit left or right and costs 1 energy. A wall at x > 0 is crossed every time you step between x - 1 and x, in either direction. A wall at x < 0 is crossed every time you step between x + 1 and x. Each crossing costs that wall's cost again, on top of the step. Your total spend can never go over energy, and you may stop anywhere.

Implement:

def max_walls(energy: int, positions: list[int], costs: list[int]) -> int:
    ...

Return the largest number of distinct walls you can cross.

Constraints

• 0 <= len(positions) == len(costs) <= 10^5
• -10^9 <= positions[k] <= 10^9, positions[k] != 0, all distinct
• 0 <= costs[k] <= 10^9, 0 <= energy <= 10^15

Example 1

energy = 10, positions = [3, -2, 6], costs = [2, 1, 1] → 2

Walk right to 6: 6 steps plus costs 2 + 1 = 9. Crossing -2 and 3 instead needs 11.

Example 2

energy = 15, same walls → 3

Walk left to -2 and back to 0 (2 * (2 + 1) = 6), then right to 6 (9). Total: 15.

Reconstructed from the reported question; details may differ from what interviewers ask.