<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>

"""
Input: bombs = [[2,1,3],[6,1,4]]
Output: 2
"""

import math


class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        def bomb_overlap(bomb1, bomb2):
            x1, y1, r1 = bomb1
            x2, y2, r2 = bomb2
            # Calculate the distance between the centers of the circles
            distance = math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)

            # Check if the distance is less than or equal to the sum of the radii
            if distance <= r1 + r2:
                return True
            else:
                return False

        def create_graph(bombs):
            graph = collections.defaultdict(list)
            n = len(bombs)

            for i in range(n):
                for j in range(i + 1, n):
                    bomb1 = bombs[i]
                    bomb2 = bombs[j]
                    x1, y1, r1 = bomb1
                    x2, y2, r2 = bomb2
                    # Calculate the distance between the centers of the circles
                    distance = math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)

                    # Check if the distance is less than or equal to the sum of the radii
                    if distance <= r1:
                        graph[i].append(j)
                    if distance <= r2:
                        graph[j].append(i)

            return graph

        def dfs(bombs, i, graph, visited):
            path_len = 0
            if i in visited:
                return path_len

            visited.add(i)

            for neighbor in graph[i]:
                path_len = max(path_len, dfs(bombs, neighbor, graph, visited) + 1)

            return len(visited)

        graph = create_graph(bombs)
        path_len = 1

        for b in range(len(bombs)):
            path_len = max(path_len, dfs(bombs, b, graph, set()))

        return path_len

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