Introduction

Last Stone Weight means:

  • repeatedly smashing the two heaviest stones until one or none remains

Rules:

If x == yBoth stones are destroyed.

If x != y
New stone:
y - x

Goal:

  • find final remaining stone

Example:

Stones:[2,7,4,1,8,1]

Output:
1

Explanation:

Repeated smashing leaves one stone with weight 1.

This problem is one of the most important applications of:

Max Heap

Constraints

1 <= Stones Length <= 10^5

Approach : Max Heap

Explanations:

Explanation:

The idea is:

  • always access
    largest stones quickly
  • Max Heap provides
    efficient retrieval

Steps:

  1. Create Max Heap.
  2. Remove largest stone.
  3. Remove second largest stone.
  4. Smash both stones.
  5. Insert difference if needed.
  6. Continue until one stone remains.

Condition:

largest != secondLargest
Insert:
largest - secondLargest

Observation:

 Heap always keeps stones ordered by weight.

This approach:

  • avoids repeated sorting
  • efficiently finds largest stones

Dry Run

Stones:[2,7,4,1,8,1]

Heap:
[8,7,4,2,1,1]

Smash:
8 and 7

New Stone:
1

Heap:
[4,2,1,1,1]

Smash:
4 and 2

New Stone:
2

Heap:
[2,1,1,1]

Smash:
2 and 1

New Stone:
1

Heap:
[1,1,1]

Smash:
1 and 1
Destroyed

Heap:
[1]

Answer:
1

Practice :

Complexity Analysis :

Time Complexity:- O(n log n)Explanation :
Heap insertions and removals take log n time.

Space Complexity:- O(n)
Explanation :
Heap stores all stones.

Why This Problem is Important

This problem builds the foundation for:

  • Max Heap operations
  • Priority queues
  • Simulation problems
  • Efficient retrieval
  • Heap-based optimization

Real-World Applications

Heap concepts are used in:

  • Task scheduling
  • Resource allocation
  • Event processing
  • Priority systems
  • Job management

Common Beginner Mistakes

  • Sorting after every smash
  • Using Min Heap instead of Max Heap
  • Forgetting equal-stone case
  • Incorrect difference calculation
  • Ignoring heap optimization

Interview Tip

Interviewers often expect:

  • heap property understanding
  • Max Heap explanation
  • simulation discussion
  • complexity clarity

Always explain:

  • why largest stones are needed
  • why Max Heap is ideal
  • sorting vs heap tradeoff

Related Questions

  • Kth Largest Element
  • Top K Frequent Elements
  • Find Median from Data Stream
  • Heap Sort
  • K Closest Points to Origin

Final Takeaway

The Last Stone Weight problem is one of the most important beginner heap problems.

It teaches:

  • Max Heap usage
  • Priority Queue operations
  • simulation with heaps
  • efficient retrieval

Understanding this problem builds a strong foundation for:

  • advanced heap problems
  • priority queue algorithms
  • interview-level data structures.