Eliminate Maximum Number of Monsters

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Problem Statement

You are playing a video game where you are defending your city from a group of n monsters. You are given a 0-indexed integer array dist of size n , where dist[i] is the initial distance in kilometers of the i ^th monster from the city.

The monsters walk toward the city at a constant speed. The speed of each monster is given to you in an integer array speed of size n , where speed[i] is the speed of the i ^th monster in kilometers per minute.

You have a weapon that, once fully charged, can eliminate a single monster. However, the weapon takes one minute to charge. The weapon is fully charged at the very start.

You lose when any monster reaches your city. If a monster reaches the city at the exact moment the weapon is fully charged, it counts as a loss , and the game ends before you can use your weapon.

Return the maximum number of monsters that you can eliminate before you lose, or n if you can eliminate all the monsters before they reach the city.

Examples

Example 1

Input: dist = [1,3,4], speed = [1,1,1]
Output: 3
In the beginning, the distances of the monsters are [1,3,4]. You eliminate the first monster.
After a minute, the distances of the monsters are [X,2,3]. You eliminate the second monster.
After a minute, the distances of the monsters are [X,X,2]. You eliminate the third monster.
All 3 monsters can be eliminated.

Example 2

Input: dist = [1,1,2,3], speed = [1,1,1,1]
Output: 1
In the beginning, the distances of the monsters are [1,1,2,3]. You eliminate the first monster.
After a minute, the distances of the monsters are [X,0,1,2], so you lose.
You can only eliminate 1 monster.

Example 3

Input: dist = [3,2,4], speed = [5,3,2]
Output: 1
In the beginning, the distances of the monsters are [3,2,4]. You eliminate the first monster.
After a minute, the distances of the monsters are [X,0,2], so you lose.
You can only eliminate 1 monster.

Constraints

n == dist.length == speed.length

1 <= n <= 10 ^5

1 <= dist[i], speed[i] <= 10 ^5

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGreedy