2101. Detonate the Maximum Bombs

 https://leetcode.com/problems/detonate-the-maximum-bombs/description/

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

---

DFS, BFS both work

DFS is cleaner

initialize return to 1, increment return .. ans += dfs for every valid move

No need to backtrack, create new visiting set at start

Use Math.pow to compare distance with radius - prevent integer overflow

---

Time - O(N^ 2) - to build graph

Space - O(N ^ 2) - to hold graph

---

---

	class Solution {
	public int maximumDetonation(int[][] bombs) {
	if (bombs == null || bombs.length == 0) {
	return 0;
	}
	Set<Integer>[] graph = new Set[bombs.length];
	buildGraph(bombs, graph);
	// atleast 1
	int ans = 1;
	// start from each node
	for (int i = 0; i < graph.length && ans < graph.length; i++) {
	// new visited for each start point, no need to backtrack
	Set<Integer> visited = new HashSet<Integer>();
	visited.add(i);
	ans = Math.max(ans, dfs(graph, i, visited));
	}
	return ans;
	}
	private void buildGraph(int[][] bombs, Set<Integer>[] graph) {
	for (int i = 0; i < bombs.length; i++) {
	graph[i] = new HashSet<Integer>();
	for (int j = 0; j < bombs.length; j++) {
	if (i == j) {
	continue;
	}
	// if target is within radius, use Math.pow to work with double, prevent integer overflow
	if ((Math.pow(bombs[i][0] - bombs[j][0], 2) + Math.pow(bombs[i][1] - bombs[j][1], 2)) <= Math.pow(bombs[i][2], 2)) {
	graph[i].add(j);
	}
	}
	}
	}
	private int dfs(Set<Integer>[] graph, int i, Set<Integer> visited) {
	int ans = 1;
	for (int target: graph[i]) {
	if (!visited.contains(target)) {
	visited.add(target);
	ans += dfs(graph, target, visited);
	}
	}
	return ans;
	}
	}

view raw 2101.DetonateTheMaximumBombsDFS.java hosted with ❤ by GitHub

	class Solution {
	public int maximumDetonation(int[][] bombs) {
	if (bombs == null || bombs.length == 0) {
	return 0;
	}
	Set<Integer>[] graph = new Set[bombs.length];
	buildGraph(bombs, graph);
	// atleast 1
	int ans = 1;
	// start from each node
	for (int i = 0; i < graph.length && ans < graph.length; i++) {
	// count 1, each new starting point
	int count = 1;
	Set<Integer> visited = new HashSet<Integer>();
	visited.add(i);
	Queue<Integer> q = new LinkedList<Integer>();
	q.offer(i);
	while (!q.isEmpty()) {
	int curr = q.poll();
	for (int neighbor: graph[curr]) {
	if (!visited.contains(neighbor)) {
	visited.add(neighbor);
	// new valid target
	count++;
	q.offer(neighbor);
	}
	}
	}
	ans = Math.max(ans, count);
	}
	return ans;
	}
	private void buildGraph(int[][] bombs, Set<Integer>[] graph) {
	for (int i = 0; i < bombs.length; i++) {
	graph[i] = new HashSet<Integer>();
	for (int j = 0; j < bombs.length; j++) {
	if (i == j) {
	continue;
	}
	// if target is within radius, use Math.pow to work with double, prevent integer overflow
	if ((Math.pow(bombs[i][0] - bombs[j][0], 2) + Math.pow(bombs[i][1] - bombs[j][1], 2)) <= Math.pow(bombs[i][2], 2)) {
	graph[i].add(j);
	}
	}
	}
	}
	}

view raw 2101.DetonateTheMaximumBombsBFS.java hosted with ❤ by GitHub