Python DSA (Data Structures and Algorithms) Syllabus

Python DSA (Data Structures and Algorithms) Notes

1. Introduction to DSA in Python

• Data Structure: Organizes data for efficient operations.
• Algorithm: A set of steps to solve a problem.
• Why DSA? Improves efficiency and optimizes performance.

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2. Time and Space Complexity

• Big-O Notation: Measures algorithm performance.
• Common Complexities:
  • O(1) – Constant Time
  • O(log n) – Logarithmic Time
  • O(n) – Linear Time
  • O(n log n) – Log-Linear Time
  • O(n²) – Quadratic Time
  • O(2ⁿ) – Exponential Time
• Example:

  
  def constant_time(arr):
      return arr[0]  # O(1)
  
  def linear_time(arr):
      for item in arr:  # O(n)
          print(item)
  

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3. Lists and Strings

Lists (Dynamic Arrays)

• Declaration: arr = [1, 2, 3, 4]
• Operations:

  
  arr.append(5)  # O(1)
  arr.insert(1, 10)  # O(n)
  arr.remove(3)  # O(n)
  arr.pop()  # O(1)
  

Strings

• Immutable in Python
• Common Operations:

  
  s = "Hello"
  print(s[0])  # Accessing character
  print(s[::-1])  # Reversing string
  print(s.upper())  # Convert to uppercase
  

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4. Linked List

• Singly Linked List

  class Node:
      def __init__(self, data):
          self.data = data
          self.next = None
  
  class LinkedList:
      def __init__(self):
          self.head = None
  

• Operations: Insertion, Deletion, Traversal, Reversal.

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5. Stacks and Queues

Stack (LIFO)

stack = []
stack.append(10)  # Push
stack.pop()  # Pop

Queue (FIFO)

from collections import deque
queue = deque()
queue.append(10)  # Enqueue
queue.popleft()  # Dequeue

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6. Recursion

• Factorial Example

  def factorial(n):
      if n == 0:
          return 1
      return n * factorial(n - 1)
  

• Tail Recursion vs Head Recursion

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7. Trees

• Binary Tree

  class TreeNode:
      def __init__(self, value):
          self.value = value
          self.left = None
          self.right = None
  

• Traversals:
  • Inorder (L, Root, R)
  • Preorder (Root, L, R)
  • Postorder (L, R, Root)

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8. Graphs

• Representations:

  graph = {
      'A': ['B', 'C'],
      'B': ['A', 'D', 'E'],
      'C': ['A', 'F'],
      'D': ['B'],
      'E': ['B', 'F'],
      'F': ['C', 'E']
  }
  

• Graph Traversals:
  • BFS (Breadth-First Search)
  • DFS (Depth-First Search)

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9. Searching and Sorting Algorithms

• Searching:

  def binary_search(arr, target):
      left, right = 0, len(arr) - 1
      while left <= right:
          mid = (left + right) // 2
          if arr[mid] == target:
              return mid
          elif arr[mid] < target:
              left = mid + 1
          else:
              right = mid - 1
      return -1
  

• Sorting Algorithms:

  • Bubble Sort

  def bubble_sort(arr):
      n = len(arr)
      for i in range(n):
          for j in range(0, n-i-1):
              if arr[j] > arr[j+1]:
                  arr[j], arr[j+1] = arr[j+1], arr[j]
  

  • Merge Sort

  def merge_sort(arr):
      if len(arr) > 1:
          mid = len(arr) // 2
          L, R = arr[:mid], arr[mid:]
          merge_sort(L)
          merge_sort(R)
          i = j = k = 0
          while i < len(L) and j < len(R):
              if L[i] < R[j]:
                  arr[k] = L[i]
                  i += 1
              else:
                  arr[k] = R[j]
                  j += 1
              k += 1
  

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10. Dynamic Programming (DP)

• Memoization (Top-Down)

  def fib(n, memo={}):
      if n in memo:
          return memo[n]
      if n <= 1:
          return n
      memo[n] = fib(n-1, memo) + fib(n-2, memo)
      return memo[n]
  

• Tabulation (Bottom-Up)

  def fib(n):
      dp = [0, 1]
      for i in range(2, n+1):
          dp.append(dp[i-1] + dp[i-2])
      return dp[n]
  

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11. Hashing

• Using Python Dictionary

  hashmap = {}
  hashmap["name"] = "Alice"
  print(hashmap["name"])  # Output: Alice

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