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Core Implementation

Python offers several ways to implement arrays:

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Built-in Lists (Dynamic Arrays)

# Basic list implementation
numbers = [1, 2, 3, 4, 5]

# Common operations
numbers.append(6)        # Add element
numbers.pop()           # Remove last element
numbers.insert(0, 0)    # Insert at index
numbers.remove(3)       # Remove specific element
numbers[2] = 10         # Update element
element = numbers[1]    # Access element

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NumPy Arrays (Static Arrays)

import numpy as np

# Fixed-size array
arr = np.array([1, 2, 3, 4, 5])

# Multi-dimensional array
matrix = np.array([[1, 2, 3], [4, 5, 6]])

# Array with specific data type
int_array = np.array([1, 2, 3], dtype=np.int32)

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Array Module (Homogeneous Arrays)

from array import array

# Type code 'i' for signed integers
int_array = array('i', [1, 2, 3, 4, 5])

# Type code 'd' for double-precision floats
float_array = array('d', [1.0, 2.0, 3.0])

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Implementation Variations

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1. Circular Array

class CircularArray:
    def __init__(self, size):
        self.size = size
        self.array = [None] * size
        self.head = 0
        self.tail = 0
        self.count = 0
    
    def enqueue(self, item):
        if self.count == self.size:
            raise Exception("Array is full")
        self.array[self.tail] = item
        self.tail = (self.tail + 1) % self.size
        self.count += 1
    
    def dequeue(self):
        if self.count == 0:
            raise Exception("Array is empty")
        item = self.array[self.head]
        self.head = (self.head + 1) % self.size
        self.count -= 1
        return item

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2. Dynamic Array (Manual Implementation)

class DynamicArray:
    def __init__(self):
        self.array = [None] * 16
        self.size = 0
        self.capacity = 16
    
    def append(self, item):
        if self.size == self.capacity:
            self._resize(self.capacity * 2)
        self.array[self.size] = item
        self.size += 1
    
    def _resize(self, new_capacity):
        new_array = [None] * new_capacity
        for i in range(self.size):
            new_array[i] = self.array[i]
        self.array = new_array
        self.capacity = new_capacity

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Time Complexities

OperationDynamic Array (List)Static Array (NumPy)Circular Array
Access (index)O(1)O(1)O(1)
AppendO(1)*N/AO(1)
Insert (beginning)O(n)N/AN/A
Insert (middle)O(n)N/AN/A
Delete (beginning)O(n)N/AO(1)**
Delete (middle)O(n)N/AN/A
Search (unsorted)O(n)O(n)O(n)
Search (sorted)O(log n)***O(log n)***O(n)
* Amortized time complexity ** For circular array queue implementation *** Using binary search if array is sorted

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Space Complexities

ImplementationSpace ComplexityAdditional Notes
Dynamic Array (List)O(n)Typically allocates 2x needed space
Static Array (NumPy)O(n)Fixed size, more memory efficient
Circular ArrayO(n)Fixed size with constant extra space
Multi-dimensionalO(n*m)For 2D array with n rows and m columns

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Common Data Structure Patterns

  1. Two Pointer Technique
    • Fast and slow pointers
    • Start and end pointers
    • Sliding window
  2. Sliding Window
    • Fixed size window
    • Variable size window
    • Multiple windows
  3. Prefix Sum
    • Cumulative sum array
    • Difference array
  4. Kadane’s Algorithm Pattern
    • Maximum subarray
    • Dynamic programming with arrays
  5. Dutch National Flag
    • Three-way partitioning
    • Quick sort partitioning
  6. Cyclic Sort
    • In-place sorting
    • Missing/duplicate numbers

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Edge Cases to Consider

  1. Empty Array
arr = []
# Handle: if not arr: return None
  1. Single Element
arr = [1]
# Handle: if len(arr) == 1: return arr[0]
  1. Array Size Limits
# Memory limit exceeded
large_arr = [0] * (10**8)  # May cause MemoryError
  1. Integer Overflow
# Python handles automatically, but consider for other languages
max_int = 2**31 - 1
arr = [max_int, max_int]
# sum(arr) might overflow in other languages
  1. Duplicate Elements
arr = [1, 1, 2, 2, 3, 3]
# Consider: set(arr) for unique elements

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Optimization Techniques

  1. Pre-allocation
# Bad
arr = []
for i in range(1000000):
    arr.append(i)

# Good
arr = [0] * 1000000
for i in range(1000000):
    arr[i] = i
  1. List Comprehension
# Bad
squares = []
for i in range(1000):
    squares.append(i * i)

# Good
squares = [i * i for i in range(1000)]
  1. Using NumPy for Numerical Operations
# Bad
arr = [1, 2, 3, 4, 5]
squared = [x * x for x in arr]

# Good
import numpy as np
arr = np.array([1, 2, 3, 4, 5])
squared = arr ** 2

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Memory Management

  1. Garbage Collection
# Release memory explicitly
large_arr = [0] * 1000000
del large_arr  # Marks for garbage collection
  1. Memory Views
from memory_view import memoryview
# Create a memory view of an array
numbers = bytearray(b'Hello')
view = memoryview(numbers)
  1. Array Slicing
# Bad (creates copy)
large_arr = list(range(1000000))
subset = large_arr[:]

# Good (view)
subset = large_arr  # Reference
# or
subset = memoryview(large_arr)

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Performance Considerations

  1. Array Copy vs Reference
# Shallow copy (reference)
arr1 = [1, 2, 3]
arr2 = arr1  # Reference, changes affect both

# Deep copy (independent)
import copy
arr2 = copy.deepcopy(arr1)  # Independent copy
  1. Batch Processing
# Process in batches for large arrays
BATCH_SIZE = 1000
large_array = list(range(1000000))

for i in range(0, len(large_array), BATCH_SIZE):
    batch = large_array[i:i + BATCH_SIZE]
    # Process batch

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Common Pitfalls

  1. List Reference Pitfall
# Common mistake
rows = [[0] * 3] * 3  # Creates references
rows[0][0] = 1  # Modifies all rows

# Correct way
rows = [[0] * 3 for _ in range(3)]  # Independent lists
  1. Index Out of Range
arr = [1, 2, 3]
# Avoid direct access without bounds checking
try:
    value = arr[5]  # IndexError
except IndexError:
    value = None
  1. Memory Leak in Circular References
# Potential memory leak
class Node:
    def __init__(self):
        self.ref = None

node1 = Node()
node2 = Node()
node1.ref = node2
node2.ref = node1
# Clear references when done
node1.ref = None
node2.ref = None