Detonate the Maximum Bombs

Detonate the Maximum Bombs is a Medium Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Graph Traversal Patterns (DFS & BFS) pattern, in the Graph DFS - Connected Components / Island Counting subpattern.

Problem statement

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 0-indexed 2D integer array bombs where bombs[i] = [xi, yi, ri]. xi and yi denote the X-coordinate and Y-coordinate 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 <= 105

Topics and companies

Topics: Array, Math, Depth-First Search, Breadth-First Search, Graph, Geometry.

How to practise Detonate the Maximum Bombs on Thita.ai

Starter code is provided in C, C#, C++, Go, Java, JavaScript and Python. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(|V|^2 + |V| * |E|) time and O(|V| + |E|) space.

Open Detonate the Maximum Bombs in the code editor, or read the Detonate the Maximum Bombs editorial for a worked solution with its approach and complexity analysis.

Where Detonate the Maximum Bombs sits in the DSA pattern sheet

Problems related to Detonate the Maximum Bombs

Other problems that use the same Graph DFS - Connected Components / Island Counting and Graph Traversal Patterns (DFS & BFS) techniques:

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