Module 2: Technical Preparation - Advanced Challenges 2

Building on the foundation established in Module 1, this module introduces more advanced algorithm techniques and data structures commonly tested in technical interviews for data science positions. These advanced concepts will help you tackle more complex problems and optimize your solutions for efficiency.

Technical interviews for data science roles often include questions that assess both your algorithmic thinking and your understanding of data structures. This module will prepare you for these challenges by focusing on tree traversal, graph algorithms, dynamic programming, and efficient data structures like hash tables and heaps.

By the end of this module, you'll be equipped with advanced problem-solving strategies and optimization techniques that will help you stand out in technical interviews and significantly improve your GCA performance.

We strongly encourage you to click through and study the resource links provided under each bullet point for any algorithm topics you're not fully comfortable with. These carefully selected resources cover dynamic programming, graph algorithms, and advanced data structures that form the foundation for technical interviews. Taking the time to review these materials and researching more on your own now will significantly strengthen your understanding and improve your problem-solving capabilities during coding challenges.

Dynamic Programming

Dynamic programming is a powerful technique for solving problems with overlapping subproblems and optimal substructure. Key concepts include:

def fibonacci(n, memo={}):
    # Base cases
    if n <= 1:
        return n
    
    # Check if already computed
    if n in memo:
        return memo[n]
    
    # Compute and store result
    memo[n] = fibonacci(n-1, memo) + fibonacci(n-2, memo)
    return memo[n]

Graph Algorithms

Graphs represent connections between objects and are used in many real-world applications. Important graph algorithms include:

def dfs(graph, start, visited=None):
    if visited is None:
        visited = set()
    
    # Mark current node as visited
    visited.add(start)
    print(start, end=' ')
    
    # Recur for all adjacent vertices
    for neighbor in graph[start]:
        if neighbor not in visited:
            dfs(graph, neighbor, visited)
    
    return visited

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

dfs(graph, 'A')  # Output: A B D E F C

Trees and Tree Traversal

Trees are hierarchical data structures that are widely used in computer science. Common tree operations include:

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def inorder_traversal(root):
    result = []
    if root:
        # First recur on left child
        result.extend(inorder_traversal(root.left))
        # Then append the data of node
        result.append(root.val)
        # Finally recur on right child
        result.extend(inorder_traversal(root.right))
    return result

def level_order_traversal(root):
    if not root:
        return []
    
    result = []
    queue = [root]
    
    while queue:
        level_size = len(queue)
        level = []
        
        for _ in range(level_size):
            node = queue.pop(0)
            level.append(node.val)
            
            if node.left:
                queue.append(node.left)
            if node.right:
                queue.append(node.right)
                
        result.append(level)
        
    return result

Hash Tables and Heaps

These data structures enable efficient operations for specific use cases:

class MinHeap:
    def __init__(self):
        self.heap = []
        
    def parent(self, i):
        return (i - 1) // 2
        
    def left_child(self, i):
        return 2 * i + 1
    
    def right_child(self, i):
        return 2 * i + 2
        
    def insert(self, value):
        self.heap.append(value)
        self._sift_up(len(self.heap) - 1)
        
    def extract_min(self):
        if not self.heap:
            return None
            
        min_value = self.heap[0]
        last_element = self.heap.pop()
        
        if self.heap:
            self.heap[0] = last_element
            self._sift_down(0)
            
        return min_value
        
    def _sift_up(self, i):
        parent = self.parent(i)
        if i > 0 and self.heap[i] < self.heap[parent]:
            self.heap[i], self.heap[parent] = self.heap[parent], self.heap[i]
            self._sift_up(parent)
            
    def _sift_down(self, i):
        smallest = i
        left = self.left_child(i)
        right = self.right_child(i)
        
        if left < len(self.heap) and self.heap[left] < self.heap[smallest]:
            smallest = left
            
        if right < len(self.heap) and self.heap[right] < self.heap[smallest]:
            smallest = right
            
        if smallest != i:
            self.heap[i], self.heap[smallest] = self.heap[smallest], self.heap[i]
            self._sift_down(smallest)

Assignment Overview

For this assignment, you'll tackle more complex algorithm problems on LeetCode to further develop your problem-solving abilities and prepare for advanced technical interview questions.

Requirements

1. Complete the following problems on LeetCode:
   Sliding Window Maximum Find the maximum element in each sliding window of size k.
   Coin Change II Count the number of ways to make change for a given amount.
   Minimum Size Subarray Sum Find the minimum length subarray with a sum at least k.
   Maximum Product Subarray Find the contiguous subarray with the largest product.
   Binary Tree Maximum Path Sum Find the maximum path sum in a binary tree.
2. For each problem:
   • Document your approach using the REACTO framework
   • Analyze the time and space complexity of your solution
   • Identify the key data structures and algorithms used
   • Submit screenshots of your solution code

Advanced Algorithm Resources

Dynamic Programming

Data Structures

Interview Preparation