DSA Module 10: Min-Heap & Priority Queue

## Min-Heap Properties & Top-K Extraction

Min-heaps ensure root element is always the minimum value.

```python
import heapq

nums = [5, 1, 8, 3]
heapq.heapify(nums) # Transform to Min-Heap in O(N) time
min_val = heapq.heappop(nums) # Returns 1 in O(log N) time
```

MIN-HEAP TREE INVARIANT:
          ( 1 )   ◄── Root is absolute minimum
         /     \
      ( 3 )   ( 8 )
     /
  ( 5 )

• Assuming heapify sorts array completely (heapify enforces parent <= children, not full sorting).

import heapq
def find_kth_largest(nums, k):
    return heapq.nlargest(k, nums)[-1]

Extracts K largest elements efficiently using heap.

What is the time complexity of popping the minimum element from a Min-Heap of size N?