How do you solve Detonate the Maximum Bombs on LeetCode?

Detonate the Maximum Bombs (LeetCode #2101) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n²) time complexity and O(n) space complexity. Key insight: Modeling the problem as a graph helps in understanding the relationships between bombs.

What is the brute force solution for Detonate the Maximum Bombs?

The brute force approach for Detonate the Maximum Bombs is Brute Force, with O(n²) time complexity and O(1) space complexity. We can start by detonating each bomb one by one and see how many bombs can be detonated as a result. This approach is straightforward but can be slow because we will check the effect of each bomb on all others. The optimal Optimal Solution approach improves this to O(n²).

What algorithm or data structure is used to solve Detonate the Maximum Bombs?

Detonate the Maximum Bombs uses the following concepts: Array, Math, Depth-First Search, Breadth-First Search, Graph Theory, Geometry. The recommended patterns to study are: Graph Theory, Depth-First Search, Adjacency List.

What are the interview tips for Detonate the Maximum Bombs?

Clearly explain your thought process while building the graph. Discuss the trade-offs between the brute force and optimal approaches. Practice DFS and graph-related problems to become comfortable with the concepts.

What are common mistakes when solving Detonate the Maximum Bombs?

Forgetting to check if a bomb has already been visited during DFS. Not properly building the adjacency list for the graph.

#2101

Detonate the Maximum Bombs

Medium

ArrayMathDepth-First SearchBreadth-First SearchGraph TheoryGeometryGraph TheoryDepth-First SearchAdjacency List

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n²)
Space	O(1)	O(n)

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Intuition

Time O(n²)Space O(n)

We can model the bombs as a directed graph where each bomb is a node and an edge exists from bomb A to bomb B if A can detonate B. We can use Depth-First Search (DFS) to explore this graph efficiently.

⚙️

Algorithm

3 steps

1Step 1: Create an adjacency list to represent the graph of bombs based on their ranges.
2Step 2: For each bomb, perform a DFS to count how many bombs can be detonated starting from that bomb.
3Step 3: Track the maximum count of detonated bombs across all DFS calls.

solution.py29 lines

1# Full working Python code
2from math import sqrt
3from collections import defaultdict
4
5def detonateMaximumBombs(bombs):
6    n = len(bombs)
7    graph = defaultdict(list)
8
9    # Build the graph
10    for i in range(n):
11        for j in range(n):
12            if i != j and in_range(bombs[i], bombs[j]):
13                graph[i].append(j)
14
15    def in_range(b1, b2):
16        return sqrt((b1[0] - b2[0])**2 + (b1[1] - b2[1])**2) <= b1[2]
17
18    def dfs(bomb_index, visited):
19        count = 1  # Current bomb is counted
20        visited.add(bomb_index)
21        for neighbor in graph[bomb_index]:
22            if neighbor not in visited:
23                count += dfs(neighbor, visited)
24        return count
25
26    max_bombs = 0
27    for i in range(n):
28        max_bombs = max(max_bombs, dfs(i, set()))
29    return max_bombs

ℹ

Complexity note: The time complexity remains O(n²) due to the nested loop for building the graph. However, the space complexity is O(n) because we are storing the adjacency list for the graph.

1Modeling the problem as a graph helps in understanding the relationships between bombs.
2Using DFS allows us to efficiently explore all possible detonations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.