<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>

import math
from collections import defaultdict
class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        def getEuclideanDist(x1,y1,x2,y2):
            return math.sqrt((x1-x2)**2 + (y1-y2)**2)
        adjList = defaultdict(set)      # bomb index to those it affects
        for i in range(len(bombs)):
            x1, y1, r = bombs[i]
            for j in range(len(bombs)):
                if i == j: continue
                x2, y2, _ = bombs[j]
                if getEuclideanDist(x1,y1,x2,y2) <= r:
                    adjList[i].add(j)
        ret = 0
        for i in range(len(bombs)):
            visited = set({})
            toVisit = set({i})
            while toVisit:
                newVisit = set({})
                for bomb in toVisit:
                    visited.add(bomb)
                    for b in adjList[bomb]:
                        if b not in visited and b not in toVisit and b not in newVisit:
                            newVisit.add(b)
                toVisit = newVisit
            ret = max(ret, len(visited))
        return ret




        # UNION FIND DOES NOT WORK BECAUSE OF DIRECTED NATURE OF PROBLEM, one bomb affects the other but the other way around is not necessarily true
        # union find algorithm for bombs
        # return the max number of a union found
        bombToParent = {} # index to parent index
        for i in range(len(bombs)):
            bombToParent[i] = i
        depth = {}          # depth of the parent tree
        for i in range(len(bombs)):
            depth[i] = 1

        def getParent(i):
            if bombToParent[i] != i:
                bombToParent[i] = getParent(bombToParent[i])
            return bombToParent[i]
        
        def mergeParents(a, b):
            aParent, bParent = getParent(a), getParent(b)
            if depth[aParent] > depth[bParent]:
                bombToParent[bParent] = aParent
            elif depth[bParent] > depth[aParent]:
                bombToParent[aParent] = bParent
            else:
                bombToParent[bParent] = aParent
                depth[aParent] += 1

        for i, b in enumerate(bombs):
            x1, y1, r = b
            for j, b2 in enumerate(bombs):
                if i == j: continue
                # we will have to test each bomb with another, and merge as we go
                x2, y2, _ = b2
                if getEuclideanDist(x1,y1,x2,y2) <= r:
                    mergeParents(i, j)
        
        counts = defaultdict(int)
        ret = 0
        for i in range(len(bombs)):
            parent = getParent(i)
            counts[parent] += 1
            ret = max(ret, counts[parent])

        print(bombToParent)
        return ret
615