Manage Prioritized Tasks with a Heap-based Priority Queue

import heapq

class PriorityQueue:
    def __init__(self):
        self._queue = []
        self._index = 0 # Used to ensure stable ordering for items with same priority

    def push(self, item, priority):
        # priority is negative to make it a min-heap (lower number = higher priority)
        # _index is used to break ties if priorities are equal (FIFO for same priority)
        heapq.heappush(self._queue, (-priority, self._index, item))
        self._index += 1

    def pop(self):
        if not self._queue:
            raise IndexError("pop from empty priority queue")
        # Retrieve item with highest priority (lowest negative priority value)
        priority, _, item = heapq.heappop(self._queue)
        return item

    def is_empty(self):
        return len(self._queue) == 0

    def size(self):
        return len(self._queue)

# Example Usage: Task Scheduler
task_queue = PriorityQueue()

print("Adding tasks...")
task_queue.push("Send welcome email", 3) # Low priority
task_queue.push("Process critical payment", 1) # High priority
task_queue.push("Update user profile", 2) # Medium priority
task_queue.push("Generate daily report", 3) # Another low priority task

print("
Processing tasks by priority:")
while not task_queue.is_empty():
    next_task = task_queue.pop()
    print(f"Processing: {next_task}")

# Expected Output:
# Adding tasks...
# 
# Processing tasks by priority:
# Processing: Process critical payment
# Processing: Update user profile
# Processing: Send welcome email
# Processing: Generate daily report