Detonate the Maximum Bombs

class Solution {
    public int maxDetonations(int[][] bombs) {
        Map<Integer, List<Integer>> adjacencyList = new HashMap<>();
        int bombCount = bombs.length;

        // Building the adjacency list for each bomb
        for (int i = 0; i < bombCount; i++) {
            for (int j = 0; j < bombCount; j++) {
                int xi = bombs[i][0], yi = bombs[i][1], radius = bombs[i][2];
                int xj = bombs[j][0], yj = bombs[j][1];
                
                // Checking detonation condition
                if ((long)radius * radius >= (long)(xi - xj) * (xi - xj) + (long)(yi - yj) * (yi - yj)) {
                    adjacencyList.computeIfAbsent(i, k -> new ArrayList<>()).add(j);
                }
            }
        }
        
        int maxDetonations = 0;
        for (int i = 0; i < bombCount; i++) {
            maxDetonations = Math.max(maxDetonations, performBFS(i, adjacencyList));
        }
        
        return maxDetonations;
    }
    
    private int performBFS(int start, Map<Integer, List<Integer>> adjacencyList) {
        Queue<Integer> queue = new LinkedList<>();
        Set<Integer> seen = new HashSet<>();
        queue.add(start);
        seen.add(start);
        
        while (!queue.isEmpty()) {
            int current = queue.poll();
            for (int neighbor : adjacencyList.getOrDefault(current, new ArrayList<>())) {
                if (!seen.contains(neighbor)) {
                    seen.add(neighbor);
                    queue.add(neighbor);
                }
            }
        }
        return seen.size();
    }
}

The provided Java solution implements a method to determine the maximum number of bombs that can be detonated sequentially from a given list of bombs. Each bomb has properties like coordinates and a radius, which define the area of its impact.

• The maxDetonations function takes a multidimensional array bombs where each subarray denotes a bomb's x-coordinate, y-coordinate, and detonation radius.
• A hashmap adjacencyList is constructed to represent which bombs can trigger other bombs.
• This adjacency list is populated through nested loops that compare the distance between every pair of bombs against their respective radii to determine if a detonation chain is possible.
• For each bomb, it checks whether the squared distance between it and every other bomb is less than or equal to the square of its radius. If true, the other bomb can be added to its list of triggerable bombs.
• Once the adjacency list is complete, the code initiates a breadth-first search (BFS) starting from each bomb, counting all reachable bombs to simulate the maximal detonation chain from this point.
• The performBFS helper function uses a queue and a set to manage the BFS traversal. Bombs that can be detonated by the current bomb are added to the queue unless they have already been visited.
• The maximum count of detonated bombs from all starting points reveals the required solution.

This method utilizes graph traversal and adjacency concepts to effectively manage and compute the problem. Such approaches allow handling of relational data and distance comparisons in an optimized manner through efficient data structures like hashmaps and queues.

class Solution:
    def maxDetonations(self, bombs: List[List[int]]) -> int:
        connections = collections.defaultdict(list)
        bomb_count = len(bombs)

        for idx in range(bomb_count):
            for jdx in range(bomb_count):
                if idx == jdx:
                    continue
                x1, y1, range1 = bombs[idx]
                x2, y2, _ = bombs[jdx]
                
                if range1 ** 2 >= (x1 - x2) ** 2 + (y1 - y2) ** 2:
                    connections[idx].append(jdx)
        
        def explore(start):
            deque = collections.deque([start])
            seen = set([start])
            while deque:
                current = deque.popleft()
                for neighbor in connections[current]:
                    if neighbor not in seen:
                        seen.add(neighbor)
                        deque.append(neighbor)
            return len(seen)
        
        max_detonations = 0
        for idx in range(bomb_count):
            max_detonations = max(max_detonations, explore(idx))
        
        return max_detonations

The given Python 3 script solves the problem of detonating the maximum number of bombs. The approach is to calculate how many bombs can be detonated starting from each individual bomb, and then finding the maximum among all possible starting bombs.

• The maxDetonations method begins by creating a dictionary to store connections between bombs. It then iterates through each bomb to determine which other bombs it can detonate.

• Using double loops, the script compares each bomb against all others to see if the distance between them is less than or equal to the radius of the exploding bomb. If yes, a connection is established in the connections dictionary indicating that initiating the explosion of one bomb can eventually lead to the explosion of another.

• A helper function explore uses Breadth-First Search (BFS) to count all reachable bombs from a given starting bomb. It leverages a deque and a seen set to track visited bombs, ensuring each bomb is processed once.

• Finally, the method iterates over each bomb to apply the explore function and updates the max_detonations with the maximum number of detonations found.

This approach efficiently captures the essence of the problem using graph theory concepts and BFS to explore all possible scenarios and determine the maximum number of bombs that can be detonated starting from any bomb.