K-way merge with heaps in Data Structures Theory - Mini Project: Build & Apply

K-way merge with heaps

📖 Scenario: Imagine you have several sorted lists of numbers, like different shelves of books sorted by height. You want to combine all these shelves into one big sorted shelf quickly and easily.

🎯 Goal: You will build a simple step-by-step plan to merge multiple sorted lists into one sorted list using the idea of a heap, which helps pick the smallest item fast.

📋 What You'll Learn

Create a list of sorted lists with exact numbers

Set up a helper list to track current positions in each list

Use a loop to pick the smallest next number from all lists

Complete the merged list with all numbers in order

💡 Why This Matters

🌍 Real World

Merging sorted data streams is common in databases, search engines, and file systems to combine sorted files or results efficiently.

💼 Career

Understanding k-way merge is important for software engineers working with large data, optimizing algorithms, and building efficient data processing pipelines.

1

Create the sorted lists

Create a variable called sorted_lists that holds exactly these three sorted lists: [1, 4, 7], [2, 5, 8], and [3, 6, 9].

Data Structures Theory

# Create the variable sorted_lists with the three sorted lists
# Your code here

Need a hint?

Use a list of lists to hold the sorted sequences exactly as shown.

2

Set up index pointers

Create a list called indices with three zeros to track the current position in each list inside sorted_lists.

Data Structures Theory

sorted_lists = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]
# Create the indices list with three zeros
# Your code here

Need a hint?

This list keeps track of which number to pick next from each sorted list.

3

Pick the smallest next number

Create an empty list called merged. Then use a while loop that runs while the total length of merged is less than 9. Inside the loop, find the smallest next number from the lists using indices and add it to merged. Update the corresponding index in indices.

Data Structures Theory

sorted_lists = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]
indices = [0, 0, 0]
# Create merged list and loop to pick smallest next number
# Your code here

Need a hint?

Check each list's current number using indices, pick the smallest, add it to merged, then move that list's index forward.

4

Complete the merged list

Add a final line that creates a variable called result and sets it equal to the merged list.

Data Structures Theory

sorted_lists = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]
indices = [0, 0, 0]
merged = []
while len(merged) < 9:
    min_val = None
    min_list = -1
    for i in range(3):
        if indices[i] < len(sorted_lists[i]):
            val = sorted_lists[i][indices[i]]
            if min_val is None or val < min_val:
                min_val = val
                min_list = i
    merged.append(min_val)
    indices[min_list] += 1
# Set result equal to merged
# Your code here

Need a hint?

This final step just saves the merged list into a variable named result.