3661 - Maximum Walls Destroyed by Robots.

Hard

There is an endless straight line populated with some robots and walls. You are given integer arrays robots, distance, and walls:

• robots[i] is the position of the <code>i^th</code> robot.

• distance[i] is the maximum distance the <code>i^th</code> robot's bullet can travel.

• walls[j] is the position of the <code>j^th</code> wall.

Every robot has one bullet that can either fire to the left or the right at most distance[i] meters.

A bullet destroys every wall in its path that lies within its range. Robots are fixed obstacles: if a bullet hits another robot before reaching a wall, it immediately stops at that robot and cannot continue.

Return the maximum number of unique walls that can be destroyed by the robots.

Notes:

• A wall and a robot may share the same position; the wall can be destroyed by the robot at that position.

• Robots are not destroyed by bullets.

Example 1:

Input: robots = 4, distance = 3, walls = 1,10

Output: 1

Explanation:

• robots[0] = 4 fires left with distance[0] = 3, covering [1, 4] and destroys walls[0] = 1.

• Thus, the answer is 1.

Example 2:

Input: robots = 10,2, distance = 5,1, walls = 5,2,7

Output: 3

Explanation:

• robots[0] = 10 fires left with distance[0] = 5, covering [5, 10] and destroys walls[0] = 5 and walls[2] = 7.

• robots[1] = 2 fires left with distance[1] = 1, covering [1, 2] and destroys walls[1] = 2.

• Thus, the answer is 3.

Example 3:

Input: robots = 1,2, distance = 100,1, walls = 10

Output: 0

Explanation:

In this example, only robots[0] can reach the wall, but its shot to the right is blocked by robots[1]; thus the answer is 0.

Constraints:

• <code>1 <= robots.length == distance.length <= 10⁵</code>

• <code>1 <= walls.length <= 10⁵</code>

• <code>1 <= robotsi, wallsj<= 10⁹</code>

• <code>1 <= distancei<= 10⁵</code>

• All values in robots are unique

• All values in walls are unique