<p>You are given a list of bombs. The <strong>range</strong> of a bomb is defined as the area where its effect can be felt. This area is in the shape of a <strong>circle</strong> with the center as the location of the bomb.</p>

<p>The bombs are represented by a <strong>0-indexed</strong> 2D integer array <code>bombs</code> where <code>bombs[i] = [x<sub>i</sub>, y<sub>i</sub>, r<sub>i</sub>]</code>. <code>x<sub>i</sub></code> and <code>y<sub>i</sub></code> denote the X-coordinate and Y-coordinate of the location of the <code>i<sup>th</sup></code> bomb, whereas <code>r<sub>i</sub></code> denotes the <strong>radius</strong> of its range.</p>

<p>You may choose to detonate a <strong>single</strong> bomb. When a bomb is detonated, it will detonate <strong>all bombs</strong> that lie in its range. These bombs will further detonate the bombs that lie in their ranges.</p>

<p>Given the list of <code>bombs</code>, return <em>the <strong>maximum</strong> number of bombs that can be detonated if you are allowed to detonate <strong>only one</strong> bomb</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/06/desmos-eg-3.png" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> bombs = [[2,1,3],[6,1,4]]
<strong>Output:</strong> 2
<strong>Explanation:</strong>
The above figure shows the positions and ranges of the 2 bombs.
If we detonate the left bomb, the right bomb will not be affected.
But if we detonate the right bomb, both bombs will be detonated.
So the maximum bombs that can be detonated is max(1, 2) = 2.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/06/desmos-eg-2.png" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> bombs = [[1,1,5],[10,10,5]]
<strong>Output:</strong> 1
<strong>Explanation:
</strong>Detonating either bomb will not detonate the other bomb, so the maximum number of bombs that can be detonated is 1.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/07/desmos-eg1.png" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> bombs = [[1,2,3],[2,3,1],[3,4,2],[4,5,3],[5,6,4]]
<strong>Output:</strong> 5
<strong>Explanation:</strong>
The best bomb to detonate is bomb 0 because:
- Bomb 0 detonates bombs 1 and 2. The red circle denotes the range of bomb 0.
- Bomb 2 detonates bomb 3. The blue circle denotes the range of bomb 2.
- Bomb 3 detonates bomb 4. The green circle denotes the range of bomb 3.
Thus all 5 bombs are detonated.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= bombs.length&nbsp;&lt;= 100</code></li>
	<li><code>bombs[i].length == 3</code></li>
	<li><code>1 &lt;= x<sub>i</sub>, y<sub>i</sub>, r<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    int maximumDetonation(vector<vector<int>>& bombs) {
        if (bombs.size() == 1) {
            return 1;
        }
        
        const int n_bombs = bombs.size();
        
        // convert bombs into an adjacency map (graph)
        std::unordered_map<int, std::vector<int>> adjacency {};
        
        for (int i {0}; i < n_bombs; ++i) {
            for (int j {0}; j < n_bombs; ++j) {
                if (i == j) { continue; }
                
                if (inRadiusOf(bombs[i], bombs[j])) {
                    adjacency[i].push_back(j);
                }
            }
        }
        
        // Now, perform DFS at each node to find the most detonations.
        // Note: If a node is "seen", we don't need to check that node as a root,
        // As it would mean that another node would trigger it also.
        
        std::unordered_set<int> checked {};
        int max_bombs { 0 };
        
        for (int node {0}; node < n_bombs; ++node) {
            if (checked.find(node) != checked.end()) { continue; } // don't need to check this one
            
            // perform DFS
            std::unordered_set<int> seen {};
            seen.insert(node);
            max_bombs = std::max(max_bombs, dfs(node, seen, adjacency));
            
            
            for (int node : seen) {
                checked.insert(node);
            }
        }
        
        return max_bombs;
    }
    
    int dfs(int node, std::unordered_set<int>& seen, std::unordered_map<int, std::vector<int>>& adjacency) {
        int total_nodes { 1 };
        
        for (int curr : adjacency[node]) {
            if (seen.find(curr) != seen.end()) { continue; } // node was already seen in this dfs.
            
            seen.insert(curr);
            total_nodes += dfs(curr, seen, adjacency); // add however many is found in the dfs.
        }
        
        return total_nodes;
    }
    
    bool inRadiusOf(const std::vector<int>& bomb, const std::vector<int>& other) {
        // whether "other" is in radius of "bomb"
        const long long squared_dist { 
            static_cast<long long>(bomb[0]-other[0]) * (bomb[0]-other[0])
            + static_cast<long long>(bomb[1]-other[1]) * (bomb[1]-other[1])
        };
        
        return squared_dist <= static_cast<long long>(bomb[2]) * bomb[2]; // radius squared
    }
};
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