Impara Sorting Algorithms for Data Engineering | Core Algorithms for Data Processing

Sorting is a foundational operation in data engineering, playing a crucial role in data pipelines, indexing, and storage optimization. When you sort data, you make downstream processing tasks—such as deduplication, merging, and range queries—much more efficient. In large-scale data systems, sorted data enables fast lookups and efficient storage formats. For example, indexes in databases are built on sorted columns, and many storage engines require sorted input for optimal performance. Understanding sorting algorithms and knowing when to apply them is essential for designing robust and scalable data workflows.


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# Quicksort: in-place, divide-and-conquer, average O(n log n), but not stable
def quicksort(arr):
    if len(arr) <= 1:
        return arr
    pivot = arr[len(arr) // 2]
    left  = [x for x in arr if x < pivot]
    middle = [x for x in arr if x == pivot]
    right = [x for x in arr if x > pivot]
    return quicksort(left) + middle + quicksort(right)

# Mergesort: stable, O(n log n), uses extra memory for merging
def mergesort(arr):
    if len(arr) <= 1:
        return arr
    mid = len(arr) // 2
    left = mergesort(arr[:mid])
    right = mergesort(arr[mid:])
    return merge(left, right)

def merge(left, right):
    result = []
    i = j = 0
    while i < len(left) and j < len(right):
        if left[i] <= right[j]:
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1
    result.extend(left[i:])
    result.extend(right[j:])
    return result

# Example usage:
data = [5, 2, 9, 1, 5, 6]
print("Quicksort:", quicksort(data))
print("Mergesort:", mergesort(data))

For small to moderate datasets that fit in memory, algorithms like quicksort and mergesort are effective. However, when faced with data that exceeds available memory, you need a different approach. External merge sort is designed for this scenario, enabling you to sort datasets much larger than your machine's RAM by breaking the task into manageable pieces.

The process begins by dividing the large dataset into chunks that fit into memory. Each chunk is loaded, sorted in-memory (using an efficient algorithm like mergesort), and then written back to disk as a sorted "run." Once all chunks are sorted, the algorithm performs a multi-way merge: it reads the smallest elements from each run, writing the merged, sorted output to a new file. This merging phase is repeated as necessary, often in multiple passes, until only one fully sorted file remains. By carefully managing memory and disk I/O, external merge sort allows you to process massive datasets efficiently, making it a critical tool in the data engineer's toolkit.


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import heapq
import numpy as np

# Simulated external merge sort: sorts a large array by chunking and merging
def external_merge_sort_array(data, chunk_size=100):
    temp_chunks = []

    # Break data into sorted chunks
    for i in range(0, len(data), chunk_size):
        chunk = list(data[i : i + chunk_size])
        chunk.sort()
        temp_chunks.append(chunk)

    # Merge sorted chunks
    return merge_chunks(temp_chunks)

def merge_chunks(chunk_list):
    # Prepare heap for k-way merge
    heap = []
    indices = [0] * len(chunk_list)

    # Initialize heap with first element of each chunk
    for idx, chunk in enumerate(chunk_list):
        if chunk:
            heapq.heappush(heap, (chunk[0], idx))

    result = []

    # Pop smallest elements and push next ones from chunks
    while heap:
        val, idx = heapq.heappop(heap)
        result.append(val)

        indices[idx] += 1
        if indices[idx] < len(chunk_list[idx]):
            next_val = chunk_list[idx][indices[idx]]
            heapq.heappush(heap, (next_val, idx))

    return result

# Usage:
# Generate a large random dataset
data = np.random.randint(0, 1000, 10000)
sorted_data = external_merge_sort_array(data, chunk_size=500)
print(sorted_data)

Study More

Major database engines, distributed frameworks like Hadoop, and large-scale ETL systems rely on external sorting. For deeper insights, explore how PostgreSQL, MySQL, and Hadoop MapReduce use external merge sort to handle massive datasets that cannot fit in memory.

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Sezione 1. Capitolo 1

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              12345678910111213141516171819202122232425262728293031323334353637
            
# Quicksort: in-place, divide-and-conquer, average O(n log n), but not stable
def quicksort(arr):
    if len(arr) <= 1:
        return arr
    pivot = arr[len(arr) // 2]
    left  = [x for x in arr if x < pivot]
    middle = [x for x in arr if x == pivot]
    right = [x for x in arr if x > pivot]
    return quicksort(left) + middle + quicksort(right)

# Mergesort: stable, O(n log n), uses extra memory for merging
def mergesort(arr):
    if len(arr) <= 1:
        return arr
    mid = len(arr) // 2
    left = mergesort(arr[:mid])
    right = mergesort(arr[mid:])
    return merge(left, right)

def merge(left, right):
    result = []
    i = j = 0
    while i < len(left) and j < len(right):
        if left[i] <= right[j]:
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1
    result.extend(left[i:])
    result.extend(right[j:])
    return result

# Example usage:
data = [5, 2, 9, 1, 5, 6]
print("Quicksort:", quicksort(data))
print("Mergesort:", mergesort(data))


              123456789101112131415161718192021222324252627282930313233343536373839404142434445
            
import heapq
import numpy as np

# Simulated external merge sort: sorts a large array by chunking and merging
def external_merge_sort_array(data, chunk_size=100):
    temp_chunks = []

    # Break data into sorted chunks
    for i in range(0, len(data), chunk_size):
        chunk = list(data[i : i + chunk_size])
        chunk.sort()
        temp_chunks.append(chunk)

    # Merge sorted chunks
    return merge_chunks(temp_chunks)

def merge_chunks(chunk_list):
    # Prepare heap for k-way merge
    heap = []
    indices = [0] * len(chunk_list)

    # Initialize heap with first element of each chunk
    for idx, chunk in enumerate(chunk_list):
        if chunk:
            heapq.heappush(heap, (chunk[0], idx))

    result = []

    # Pop smallest elements and push next ones from chunks
    while heap:
        val, idx = heapq.heappop(heap)
        result.append(val)

        indices[idx] += 1
        if indices[idx] < len(chunk_list[idx]):
            next_val = chunk_list[idx][indices[idx]]
            heapq.heappush(heap, (next_val, idx))

    return result

# Usage:
# Generate a large random dataset
data = np.random.randint(0, 1000, 10000)
sorted_data = external_merge_sort_array(data, chunk_size=500)
print(sorted_data)

Study More

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Grazie per i tuoi commenti!

Sezione 1. Capitolo 1