Detonate the Maximum Bombs


10 Prerequisite LeetCode Problems
This is about finding the maximal impact one bomb can have by potentially triggering other bombs within its range. You need to know how to traverse or inspect multiple nodes in a graph. Here are 10 simpler problems to understand how to approach this problem:
“Flood Fill” (LeetCode 733): A problem about changing the color of an image, which can be solved with breadthfirst search (BFS) or depthfirst search (DFS).
“Number of Islands” (LeetCode 200): A problem about finding the number of connected components in a binary matrix, solvable with DFS or BFS.
“Max Area of Island” (LeetCode 695): Similar to the previous problem but now with the goal to find the biggest connected component.
“Is Graph Bipartite?” (LeetCode 785): Another problem that involves traversing a graph in a certain way.
“Pacific Atlantic Water Flow” (LeetCode 417): A more complicated problem involving graph traversal.
“Number of Connected Components in an Undirected Graph” (LeetCode 323): This problem focuses on counting connected components.
“Surrounded Regions” (LeetCode 130): This problem is about flipping the values of certain nodes in a graph, given some conditions.
“Friend Circles” (LeetCode 547): This problem is about finding connected components in a graph.
“01 Matrix” (LeetCode 542): In this problem, you are asked to find the distance from every cell to its nearest zero.
“Find the Town Judge” (LeetCode 997): This problem is about analyzing a graph of trust relationships between people.
“Detonate the Maximum Bombs” also involves understanding geometric concepts and range overlap.


Problem Classification
You are given a list of bombs. The range of a bomb is defined as the area where its effect can be felt. This area is in the shape of a circle with the center as the location of the bomb.
The bombs are represented by a 0indexed 2D integer array bombs where bombs[i] = [xi, yi, ri]. xi and yi denote the Xcoordinate and Ycoordinate of the location of the ith bomb, whereas ri denotes the radius of its range.
You may choose to detonate a single bomb. When a bomb is detonated, it will detonate all bombs that lie in its range. These bombs will further detonate the bombs that lie in their ranges.
Given the list of bombs, return the maximum number of bombs that can be detonated if you are allowed to detonate only one bomb.
Example 1:
Input: bombs = [[2,1,3],[6,1,4]] Output: 2 Explanation: 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.
Example 2:
Input: bombs = [[1,1,5],[10,10,5]] Output: 1 Explanation: Detonating either bomb will not detonate the other bomb, so the maximum number of bombs that can be detonated is 1.
Example 3:
Input: bombs = [[1,2,3],[2,3,1],[3,4,2],[4,5,3],[5,6,4]] Output: 5 Explanation: 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.
Constraints:
1 <= bombs.length <= 100 bombs[i].length == 3 1 <= xi, yi, ri <= 10^5
Identifying Problem Isomorphism
The problem “Maximum Detonation of Bombs” can be mapped to “Finding the Maximum Connected Component in an Undirected Graph.”
Reasoning:
In the “Maximum Detonation of Bombs,” we’re trying to find the maximum number of bombs that can be detonated by detonating only one bomb. The connectivity of the bombs (i.e., whether one bomb can detonate another) can be represented as an undirected graph where each bomb is a node and there is an edge between two nodes if one bomb can detonate the other.
The problem of “Finding the Maximum Connected Component in an Undirected Graph” deals with finding the largest connected component (i.e., the largest group of nodes that are all directly or indirectly connected to each other) in an undirected graph.
These two problems are isomorphic because they both involve finding the maximum connected component in an undirected graph, albeit in different contexts. The concept of finding the largest connected component is the core of both problems, and the algorithms to solve them are the same.
Among the two, “Finding the Maximum Connected Component in an Undirected Graph” is simpler, as it deals directly with the graph and doesn’t require the additional step of representing the bombs and their detonation relationships as a graph.
Language Agnostic Coding Drills
Defining a class and a method: This code includes a class
Solution
and a methodmaximumDetonation
. These are fundamental concepts in objectoriented programming.Working with lists and list indexing: In Python, a list is an ordered collection of items. The method
maximumDetonation
accepts a list of lists as an argument, and the nested lists are accessed via their indices.Defining helper function within a function: The
is_connected
function is defined within themaximumDetonation
method. Understanding function scopes is crucial here.Performing mathematical calculations: The
is_connected
function performs various calculations using the Pythagorean theorem and comparison operators.Understanding the dictionary and defaultdict: The defaultdict is a dictionary subclass that provides a default value for a nonexistent key, which is utilized here to create an adjacency list
conn
.Nested looping: The code uses nested for loops to iterate over the
bombs
list.Conditional Statements: The code uses an if statement to check whether
i
is not equal toj
, and whetheris_connected(i,j)
returns True.Understanding recursive functions: The
dfs
function is a typical implementation of Depth First Search, a common algorithm in graph theory. This function is recursive, meaning it calls itself in its execution.Working with sets: Sets in Python are unordered collections of unique elements. The variable
visited
is a set used to track visited nodes in the graph.Updating variables: The
maxCount
variable is updated inside the loop to always contain the maximum count of detonations.
Arranging these units in increasing order of difficulty would result in the following order:
 Defining a class and a method
 Working with lists and list indexing
 Performing mathematical calculations
 Conditional Statements
 Updating variables
 Defining helper function within a function
 Understanding the dictionary and defaultdict
 Nested looping
 Working with sets
 Understanding recursive functions
Targeted Drills in Python
Drill 1: Define a class with a method.


Drill 2: Working with lists and list indexing.


Drill 3: Performing mathematical calculations.


Drill 4: Conditional Statements


Drill 5: Updating variables


Drill 6: Defining helper function within a function


Drill 7: Understanding the dictionary and defaultdict


Drill 8: Nested looping


Drill 9: Working with sets


Drill 10: Understanding recursive functions

