You are given a list of bombs, where each bomb has a specific location and a range of effects. The range of a bomb is defined as a circular area centered at the bomb’s location, with a radius equal to the bomb’s range. If a bomb is detonated, it will trigger all other bombs whose centers lie within its range. These triggered bombs will further detonate any bombs within their respective ranges, creating a chain reaction.

The bombs are represented by a 0-indexed 2D integer array, bombs, where:

• bombs[i] = [xi, yi, ri]:

  • xi and yi represent the X and Y coordinates of the bomb’s location.

  • ri represents the radius of the bomb’s range.

You may choose to detonate one bomb initially. Your task is to determine the maximum number of bombs that can be detonated if you start with the optimal choice of the initial bomb.

Note: A bomb will be detonated even if its location lies exactly on the boundary of another bomb’s detonation radius.

Constraints:

• $1 \leq$ bombs.length $\leq 100$

• bombs[i].length == 3

• $1\leq x_i, \space y_i, \space r_i \leq 1000$

This algorithm determines the maximum number of bombs that can be detonated in a chain reaction, given a list of bombs with their positions $(x, \space y)$ and blast radii $r$. It first builds a directed graph where an edge exists from bomb $i$ to bomb $j$ if bomb $j$ is within the blast radius of bomb $i$. Then, it uses depth-first search (DFS) to simulate the chain reaction starting from each bomb. The DFS explores how many bombs can be detonated from a starting bomb by recursively visiting all reachable bombs. All possible chains of detonated bombs are recorded, and the one with the maximum number of detonations is identified. Finally, the function returns the maximum number of bombs that can be detonated in one chain reaction.

The steps of the algorithm are as follows:

1. Create an adjacency list graph with n empty lists, where n is the number of bombs.

2. For each bomb $i,$ retrieve its coordinates $(x_1​, \space y_1​)$ and blast radius $r_1$​.
   Compare it with every other bomb $j$ by calculating the squared distance between $i$ and $j$.
   If $j$ lies within the blast radius of $i$ $((x_2​−x_1​)^2+(y_2​−y_1​)^2 \leq r_{1}^2​)$, add $j$ to graph[i].

3. Implement a depth-first search (DFS) function that:

   1. Adds the current bomb (node) to a visited set.

   2. Recursively visits all neighbors of the current node that haven’t been visited.

   3. Returns the size of the visited set, representing the number of detonated bombs.

4. For each bomb, $i$, perform a DFS starting from $i$. Calculate the number of bombs detonated and update max_detonated with the maximum value found.

5. After iterating through all bombs, return max_detonated, which holds the largest chain reaction size.

Let’s look at the following illustration to get a better understanding of the solution: