Maximum Walls Destroyed by Robots

arraybinary searchdynamic programming

Problem Statement

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 i ^th robot.

distance[i] is the maximum distance the i ^th robot's bullet can travel.

walls[j] is the position of the j ^th 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.

Examples

Example 1

Input: robots = [4], distance = [3], walls = [1,10]
Output: 1
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
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
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

1 <= robots.length == distance.length <= 10 ^5

1 <= walls.length <= 10 ^5

1 <= robots[i], walls[j] <= 10 ^9

1 <= distance[i] <= 10 ^5

All values in robots are unique

All values in walls are unique

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search