The Number of Weak Characters in the Game

Problem Description

You are playing a game that contains multiple characters, and each of the characters has two main properties: attack and defense. You are given a 2D integer array properties where properties[i] = [attack_i, defense_i] represents the properties of the i-th character in the game. A character is said to be weak if any other character has both attack and defense levels strictly greater than this character's attack and defense levels. Return the number of weak characters.

Key Insights

• A character is weak if there exists another character with strictly greater attack and defense.
• Sorting the characters by attack and defense can simplify the problem.
• Using a greedy approach can help in counting weak characters efficiently.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the array.
Space Complexity: O(n) - for storing the sorted characters if needed.

Solution

To solve this problem, we can follow these steps:

1. Sort the characters based on their attack values in ascending order. If two characters have the same attack value, sort by defense in descending order. This ensures that when we compare characters, we only need to check defenses against previously seen characters.
2. Initialize a variable to keep track of the maximum defense encountered as we iterate through the sorted characters.
3. For each character, if its defense is less than or equal to the maximum defense seen so far, it is weak.
4. Count such weak characters.

This approach leverages sorting and a single pass through the characters to efficiently determine the number of weak characters.

Code Solutions