<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:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        pass






















class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list)
        # O(N**2) build adj list
        for i in range(len(bombs)):
            for j in range(i+1, len(bombs)):
                dist = sqrt((bombs[i][0] - bombs[j][0]) ** 2 + (bombs[i][1] - bombs[j][1]) ** 2)
                if bombs[i][2] >= dist:
                    adj[tuple(bombs[i])].append(tuple(bombs[j]))
                if bombs[j][2] >= dist:
                    adj[tuple(bombs[j])].append(tuple(bombs[i]))

        # Traverse and count maximum reach
        # O(N**2)
        def bfs_old(idx):
            cnt = 0
            seen = set([tuple(bombs[idx])])
            queue = deque([bombs[idx]])
            while queue:
                x, y, r = queue.popleft()
                cnt += 1
                for neigh in adj[(x, y, r)]:
                    if neigh not in seen:
                        queue.append(neigh)
                        seen.add(neigh)
            return cnt

        def bfs_old(idx):
            cnt = 0
            seen = set([idx])
            queue = deque([bombs[idx]])
            while queue:
                x, y, r = queue.popleft()
                cnt += 1
                for neigh in adj[(x, y, r)]:
                    if neigh not in seen:
                        queue.append(neigh)
                        seen.add(neigh)
            return cnt
        
        cnt_max = 0
        for i in range(len(bombs)):
            cnt_max = max(cnt_max, bfs(i))
        return cnt_max



class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list)
        # O(N**2) build adj list
        for i in range(len(bombs)):
            for j in range(i+1, len(bombs)):
                dist = sqrt((bombs[i][0] - bombs[j][0]) ** 2 + (bombs[i][1] - bombs[j][1]) ** 2)
                if bombs[i][2] >= dist:
                    adj[i].append(j)
                if bombs[j][2] >= dist:
                    adj[j].append(i)

        # Traverse and count maximum reach
        # O(N**2)
        def bfs(idx):
            cnt = 0
            seen = set([idx])
            queue = deque([idx])
            while queue:
                idx = queue.popleft()
                x, y, r = bombs[idx]
                cnt += 1
                for idx_neigh in adj[idx]:
                    if idx_neigh not in seen:
                        queue.append(idx_neigh)
                        seen.add(idx_neigh)
            return cnt

        
        cnt_max = 0
        for i in range(len(bombs)):
            cnt_max = max(cnt_max, bfs(i))
        return cnt_max












class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list)
        for i in range(len(bombs)):
            for j in range(i+1, len(bombs)):
                dist = sqrt((bombs[i][0]-bombs[j][0])**2 + (bombs[i][1]-bombs[j][1])**2)
                if bombs[i][-1] >= dist:
                    adj[i].append(j)
                if bombs[j][-1] >= dist:
                    adj[j].append(i)

        max_len = 0
        print(adj)

        def bfs(idx):
            max_len = 0
            seen = set([idx])
            queue = deque([idx])
            while queue:
                idx = queue.popleft()
                max_len += 1

                for neigh in adj[idx]:
                    if neigh not in seen:
                        seen.add(neigh)
                        queue.append(neigh)
            return max_len
        
        for i in range(len(bombs)):
            max_len = max(max_len, bfs(i))
        return max_len

























class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list)
        for i in range(len(bombs)):
            for j in range(i+1, len(bombs)):
                x1, y1, r1 = bombs[i]
                x2, y2, r2 = bombs[j]
                dist = sqrt((x1-x2)**2 + (y1-y2)**2)
                if dist <= r1:
                    adj[i].append(j)
                if dist <= r2:
                    adj[j].append(i)

        #@lru_cache(None)
        def dp(i):
            max_depth = 1
            for neigh in adj[i]:
                if neigh not in seen:
                    seen.add(neigh)
                    max_depth += dp(neigh)
            return max_depth
        
        max_depth = 0
        for i in range(len(bombs)):
            seen = set()
            seen.add(i)
            max_depth = max(max_depth, dp(i))
        return max_depth




class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list)
        for i in range(len(bombs)):
            for j in range(i+1, len(bombs)):
                x1, y1, r1 = bombs[i]
                x2, y2, r2 = bombs[j]
                dist = sqrt((x1-x2)**2 + (y1-y2)**2)
                if dist <= r1:
                    adj[i].append(j)
                if dist <= r2:
                    adj[j].append(i)

        def dfs(i):
            ans = 1
            for neigh in adj[i]:
                if neigh not in seen:
                    seen.add(neigh)
                    ans += dfs(neigh)
            return ans
        
        ans = 0
        for i in range(len(bombs)):
            seen = set()
            seen.add(i)
            ans = max(ans, dfs(i))
        return ans

























class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list)
        for i in range(len(bombs)):
            for j in range(i+1, len(bombs)):
                x1, y1, r1 = bombs[i]
                x2, y2, r2 = bombs[j]
                dist = sqrt((x1-x2)**2+(y1-y2)**2)
                if r1 >= dist:
                    #adj[(x1,y1,r1)].append((x2, y2, r2))
                    adj[i].append(j)
                if r2 >= dist:
                    #adj[(x2,y2,r2)].append((x1, y1, r1))
                    adj[j].append(i)
        
        def dfs(node, seen):
            ans = 1
            for neigh in adj[node]:
                if neigh not in seen:
                    seen.add(neigh)
                    ans += dfs(neigh, seen)
            return ans
        
        max_depth = 0
        for i in range(len(bombs)):
            max_depth = max(max_depth, dfs(i, set([i])))
        return max_depth




















class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list)
        for i in range(len(bombs)):
            for j in range(i+1, len(bombs)):
                x1, y1, r1 = bombs[i]
                x2, y2, r2 = bombs[j]
                dist = sqrt((x1-x2)**2 + (y1-y2)**2)
                if r1 >= dist:
                    adj[i].append(j)
                if r2 >= dist:
                    adj[j].append(i)
        
        def dfs(node):
            cnt = 1
            for neigh in adj[node]:
                if neigh not in seen:
                    seen.add(neigh)
                    cnt += dfs(neigh)
            return cnt

        cnt = 0
        for i in range(len(bombs)):
            seen = set([i])
            cnt_curr = dfs(i)
            cnt = max(cnt_curr, cnt)
        return cnt























class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list)
        for i in range(len(bombs)):
            for j in range(i+1, len(bombs)):
                x1, y1, r1 = bombs[i]
                x2, y2, r2 = bombs[j]
                dist = sqrt((x1-x2)**2 + (y1-y2)**2)
                if r1 >= dist:
                    adj[i].append(j)
                if r2 >= dist:
                    adj[j].append(i)
        
        def traversal(node, visited):
            ln = 0
            for neigh in adj[node]:
                if neigh not in visited:
                    visited.add(neigh)
                    ln += traversal(neigh, visited)
            return ln + 1
        
        max_ln = 0
        for i in range(len(bombs)):
            max_ln = max(max_ln, traversal(i, set([i])))
        return max_ln















class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list) # idx --> list[idx]
        for i in range(len(bombs)):
            for j in range(i):
                x1, y1, r1 = bombs[i]
                x2, y2, r2 = bombs[j]
                dist = sqrt((x1-x2)**2 + (y1-y2)**2)
                if r1 >= dist:
                    adj[i].append(j)
                if r2 >= dist:
                    adj[j].append(i)
        
        #@lru_cache(None)
        def dfs(idx_bomb, seen):
            # return total number of bombs to be blown. 
            ans = 0
            for idx_neigh in adj[idx_bomb]:
                if idx_neigh not in seen:
                    seen.add(idx_neigh)
                    ans += dfs(idx_neigh, seen)
            return ans + 1
        
        max_n = 0
        for idx_bomb in range(len(bombs)):
            max_n = max(max_n, dfs(idx_bomb, set([idx_bomb])))
        return max_n



















class Solution:
    def maximumDetonation(self, bombs: List[List[int]]) -> int:
        adj = collections.defaultdict(list)
        for i in range(len(bombs)):
            for j in range(i):
                x1, y1, r1 = bombs[i]
                x2, y2, r2 = bombs[j]
                dist = sqrt((x1-x2)**2 + (y1-y2)**2)
                if dist <= r1:
                    adj[i].append(j)
                if dist <= r2:
                    adj[j].append(i)

        def traversal(idx_b):
            n_blow = 1
            for neigh in adj[idx_b]:
                if neigh not in seen:
                    seen.add(neigh)
                    n_blow += traversal(neigh)
            return n_blow
        
        max_n = 0
        for i in range(len(bombs)):
            seen = set([i])
            max_n = max(max_n, traversal(i))
        return max_n
18000