The Number of Weak Characters in the Game

class Solution {
public:
    int weakCharactersCount(vector<vector<int>>& props) {
        int highestAttack = 0;
        // Determine the highest attack value among all characters
        for (auto& prop : props) {
            int currentAttack = prop[0];
            highestAttack = max(highestAttack, currentAttack);
        }
            
        vector<int> topDefense(highestAttack + 2, 0);
        // Compile the best defense value for each attack level
        for (auto& prop : props) {
            int attackLevel = prop[0];
            int defenseLevel = prop[1];
                
            topDefense[attackLevel] = max(topDefense[attackLevel], defenseLevel);
        }
    
        // Update the defensive values to ensure they are maximal for increasing attack values
        for (int i = highestAttack - 1; i >= 0; i--) {
            topDefense[i] = max(topDefense[i], topDefense[i + 1]);
        }
            
        int weakCount = 0;
        // Evaluate each character to see if it is weak
        for (auto& prop : props) {
            int charAttack = prop[0];
            int charDefense = prop[1];
                
            // Character is weak if there is a stronger defense at a higher attack level
            if (charDefense < topDefense[charAttack + 1]) {
                weakCount++;
            }
        }
            
        return weakCount;
    }
};

The solution provided for counting weak characters in a game implements an effective algorithm using C++. This approach focuses on tracking characters' properties, identifying attack and defense levels, and determining the weak characters based on specific conditions.

Key Elements of the Solution:

• First, determine the highest attack value to establish the range of attack levels.
• Create a vector to track the maximum defense value that corresponds to each attack level.
• After populating the vector with the best defense values per attack level, iterate from higher to lower attack levels to ensure that each attack level stores the maximum defensive value up to that point.
• Count the number of weak characters by comparing each character’s defense against the maximized defense values for higher attack levels. A character is considered weak if its defense is less than the maximum defense for any higher attack level.

Steps Implemented in the Code:

1. Loop through the list of characters to find the maximum attack value.

2. Initialize a vector called topDefense where the index represents the attack level, and the value at each index is the highest known defense for that attack level.

3. Update topDefense with the maximum defense values directly corresponding to each attack level found.

4. Ensure that each entry in topDefense represents the maximum defensive value from that attack level to the maximum attack level by iterating backwards and updating defensively.

5. Finally, count and identify the weak characters. Check if the defense of a character is less than the stored defensive value for the next higher attack level, incrementing the count for each weak character found.

The implementation efficiently consolidates information about attack and defense, and uses this preprocessed data to rapidly assess character weaknesses, resulting in a solution that optimizes both time and space complexities.

class Solution {
    public int countWeakCharacters(int[][] attributes) {
        int highestAttack = 0;
        // Determine the highest 'attack' attribute
        for (int[] attr : attributes) {
            int currentAttack = attr[0];
            highestAttack = Math.max(highestAttack, currentAttack);
        }
            
        // Array to store the highest defense for each attack value
        int[] maxDefensePerAttack = new int[highestAttack + 2];
        for (int[] attr : attributes) {
            int currentAttack = attr[0];
            int currentDefense = attr[1];
            maxDefensePerAttack[currentAttack] = Math.max(maxDefensePerAttack[currentAttack], currentDefense);
        }
    
        // Process to ensure each spot has the maximum defense up to that point
        for (int i = highestAttack - 1; i >= 0; i--) {
            maxDefensePerAttack[i] = Math.max(maxDefensePerAttack[i], maxDefensePerAttack[i + 1]);
        }
            
        int weakCount = 0;
        for (int[] attr : attributes) {
            int currentAttack = attr[0];
            int currentDefense = attr[1];
                
            // If character's defense is less than max defense of characters with higher attack
            if (currentDefense < maxDefensePerAttack[currentAttack + 1]) {
                weakCount++;
            }
        }
            
        return weakCount;
    }
}

This Java implementation is designed to solve the problem of counting "weak characters" in a game based on their attributes. The characters are considered "weak" if there exists another character with both a strictly higher attack and defense.

The solution involves the following key steps:

1. Initialize variables to track the highest attack value among all characters.
2. Iterate through the characters to find this highest attack value.
3. Set up an array to record the maximum defense value encountered for every attack level up to the highest one observed.
4. Iterate through the characters again to populate the array with the maximum defenses for each attack level.
5. Modify the maximum defense array to ensure it maintains the property that every position holds the maximum defense value from that attack level to the highest.
6. Using the adjusted defense values, iterate again through the characters to count how many of them are "weak". A character is determined to be weak if their defense is less than the recorded maximum defense of any character with a higher attack.
7. Return the count of weak characters.

This approach ensures each character is compared against the best possible higher-attack contenders, optimizing the process by using arrays for efficient look-up and manipulation during the second scan. Importantly, the solution handles the edge cases appropriately, acknowledging when no higher attack level is available for comparison. The algorithm exhibits a comprehensible structure focused on clarity and performance.