What is the brute force approach and complexity for Asteroid Collision?

Repeatedly find the first adjacent (+, −) pair, resolve it, start over with time complexity O(N²) and space complexity O(N).

What is the optimal approach and complexity for Asteroid Collision?

Push right-movers; a left-mover pops smaller right-movers off the top in a loop with optimal time complexity O(N) and space complexity O(N).

How do you identify the pattern for Asteroid Collision?

Look for key signals in the prompt: "the smaller one explodes" indicates A new item can remove earlier ones → survivors can be popped.; "positive moves right, negative moves left" indicates Only (+ then −) meet. The direction check decides whether to pop at all.; "after all collisions" indicates One new asteroid may cause several crashes in a row → a while loop on the top..

Asteroid Collision

Medium·LeetCode #735 Pro OnlyMedium

LeetCode

Problem Statement

You are given an array asteroids of asteroids flying in a row. For each one, the absolute value is its size and the sign is its direction: positive moves right, negative moves left. All of them move at the same speed.

When two asteroids meet, the smaller one explodes. If they are the same size, both explode. Two asteroids moving in the same direction never meet.

Return the asteroids that are left after every possible collision, in their original order.

Input

An integer array asteroids (no zeros).

Output

The surviving asteroids, left to right.

Example 1

Input: asteroids = [5, 10, -5]

Output: [5, 10]

-5 crashes into 10 and explodes. 5 and 10 both move right, so they never meet.

Example 2

Input: asteroids = [8, -8]

Output: []

Same size, so both explode.

Example 3

Input: asteroids = [10, 2, -5]

Output: [10]

-5 destroys 2, then crashes into 10 and explodes.

Example 4

Input: asteroids = [3, 5, -6, 2, -1, 4]

Output: [-6, 2, 4]

-6 destroys 5 and then 3. -1 explodes against 2. -6 moves left and 2, 4 move right, so nothing else meets.

Constraints

• 2 ≤ asteroids.length ≤ 10^4
• −1000 ≤ asteroids[i] ≤ 1000
• asteroids[i] ≠ 0

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“the smaller one explodes”

→ A new item can remove earlier ones → survivors can be popped.

“positive moves right, negative moves left”

→ Only (+ then −) meet. The direction check decides whether to pop at all.

“after all collisions”

→ One new asteroid may cause several crashes in a row → a while loop on the top.

Approach Complexity Ladder

Brute Force — resolve the first crash, then rescanO(N²)O(N)

Repeatedly find the first adjacent (+, −) pair, resolve it, start over

Optimal — survivor stackO(N)O(N)

Push right-movers; a left-mover pops smaller right-movers off the top in a loop

Brute Force Intuition

Simulate it literally. Scan for the first place where a right-mover is directly followed by a left-mover. Resolve that crash by erasing the smaller one (or both if equal). Then scan again from the start. Stop when no such pair exists.

Recognition rule for this sub-pattern:

Simulate a process where new items interact with the latest survivors (collisions, path folders, min tracking).

Remember this · Stack

Trigger

Matching pairs, nested structure, undo, evaluating expressions, "the last one wins".

Think

Does each new element need to look at the most recent unresolved element?

Key question

What does an item on the stack represent, and when does it get resolved?

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