💎 Master Python Priority Queues with M.A.G.I.C.S.

A standard Queue is a line where you wait your turn. A Priority Queue is a VIP club. It doesn’t matter when you arrived; if you have the “Smallest Number” (Highest Priority), you cut the line and go straight to the front.

In Python, we use the heapq module. By default, Python creates a Min-Heap (The Smallest item is always at index 0).

Python Heapq Module, Priority Queue Python, Min Heap vs Max Heap Python, Find Kth Largest Element

The Framework

Letter	Category	Meaning	Python Syntax (heapq module)
M	Make	Create / Convert	heapify(list)
A	Add	Push item	heappush(heap, item)
G	Get	Peek smallest	heap[0]
I	Improve	Efficiency Ops	heapreplace(), heappushpop()
C	Clean	Pop smallest	heappop(heap)
S	Special	Max/Min Ops	nlargest(), nsmallest()

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🟢 1. M – MAKE (Creation)

You don’t create a special “Heap Object”. You take a normal List and “magically” rearrange it.

Operation	Syntax	Example	Result
Import	import heapq	(Required)
Empty	[]	h = []	Empty heap.
Heapify	heapify(L)	heapq.heapify(nums)	Reorders list into a heap in-place (O(n)).
Safe Copy	list(h)	backup = list(h)	Creates a copy (still a heap).

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🔵 2. A – ADD (The “Push”)

Warning: Never use .append() on a heap! It breaks the order. Always use heappush.

Operation	Syntax	Example	Result
Push	heappush(h, x)	heapq.heappush(h, 5)	Adds 5; re-sorts automatically.
Push Tuple	heappush(h, (p, val))	heapq.heappush(h, (1, "Task"))	Pro Tip: Sorts by first item (priority).

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🟡 3. G – GET (The “Peek”)

The ONLY guarantee in a heap is that index 0 is the smallest item. The rest of the list may look messy—that’s normal!

Operation	Syntax	Example	Result
Peek Min	heap[0]	smallest = h[0]	Returns smallest item (O(1)).
Peek Max?	❌	heap[-1]	WRONG! Last item is not guaranteed to be max.
Peek 2nd?	❌	heap[1]	Risky. Could be 2nd or 3rd smallest.

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🟠 4. I – IMPROVE (Efficiency)

Heaps have special moves to “Replace” the smallest item faster than doing a Pop then a Push.

Operation	Syntax	Example	Result
PushPop	heappushpop(h, x)	v = heapq.heappushpop(h, 9)	Pushes 9, then Pops smallest. (Fast).
Replace	heapreplace(h, x)	v = heapq.heapreplace(h, 9)	Pops smallest, then Pushes 9.

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🔴 5. C – CLEAN (The “Pop”)

Removing the VIP (Smallest item).

Operation	Syntax	Example	Result
Pop Min	heappop(h)	vip = heapq.heappop(h)	Removes & returns smallest item.
Clear	.clear()	h.clear()	Empties the list.

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🟣 6. S – SPECIAL (Max & N-Items)

Python does not have a “MaxHeap” class. We simulate it using math tricks.

Operation	Syntax	Example	Result
Max Heap	Invert Values	heappush(h, -x)	Store -val. When popping, convert back with -val.
N-Largest	nlargest(k, L)	top3 = heapq.nlargest(3, h)	Returns top 3 largest items.
N-Smallest	nsmallest(k, L)	bot3 = heapq.nsmallest(3, h)	Returns top 3 smallest items.

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⭐ PRO TIPS (Why use Heaps?)

Heaps are the secret to solving “Top K” problems efficiently.

Feature	Code Example	Why use it?
Priority Tasks	(1, "Fix Bug")	Use Tuples (priority_number, data). Python sorts by number first!
The Max Trick	heappush(h, -100)	Store negative numbers to simulate a MaxHeap.
Top K Items	nlargest(10, huge_list)	Much faster than sorting the whole list just to get the top 10.
Streaming	heappushpop()	Efficiently maintain a “Top 10” list on a never-ending stream of data.

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🎥 The Visual Challenge: K-th Largest Element

Problem: Find the 3rd largest number in a list of 1,000,000 items.

The Amateur Way (Sort):

Python

nums.sort()  # O(N log N) - Very Slow for huge lists!
print(nums[-3])

The Pro Way (Heap):

Python

import heapq

# O(N log K) - Much faster!
# Keeps a small heap of size 3.
top_3 = heapq.nlargest(3, nums) 
print(top_3[-1]) 

⭐ Priority Queue in Python

import queue
pq = queue.PriorityQueue()

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🔧 Priority Queue Methods

1️⃣ put(item)

pq.put(10)
pq.put(1)
pq.put(5)

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2️⃣ get()

pq.get()   # Returns smallest element

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3️⃣ empty()

pq.empty()

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4️⃣ full()

pq.full()

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5️⃣ qsize()

pq.qsize()

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🟢 Min-Heap (Default Behavior)

pq.put(3)
pq.put(1)
pq.put(2)

pq.get()  # 1

➡️ Lowest value has highest priority

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🔴 Max-Heap using PriorityQueue

Python does not directly support max-heap, but you can simulate it:

pq.put(-10)
pq.put(-5)
pq.put(-20)

print(-pq.get())  # 20

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🧠 Priority Queue with Tuples

pq.put((1, "Low"))
pq.put((0, "High"))

pq.get()  # (0, 'High')

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📊 Summary Table

Queue Type	Order
FIFO Queue	First In First Out
LIFO Queue	Last In First Out
Priority Queue	Priority Based

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⏱️ Time Complexity

Operation	Complexity
Put	O(log n)
Get	O(log n)
Peek	O(1)

Master Python Priority Queues (Heaps) in 10 Minutes: The Ultimate M.A.G.I.C.S. Cheat Sheet

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