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Data Structures and Algorithms — Introduction

Overview

Data structures and algorithms (DSA) are the vocabulary of efficient programs: how we store information and the procedures we use to transform it under time and space constraints. This section connects theory to patterns you will reuse in interviews and production systems.

Why This Exists

Every non-trivial program picks a representation (arrays, trees, graphs) and a strategy (two pointers, BFS, DP). Naming these patterns accelerates debugging, complexity analysis, and communication with peers.

How It Works

Study progresses from linear structures (Arrays, Strings, Linked lists) to constrained access (Stacks and queues), hierarchical data (Trees), relational models (Graphs), and optimization over choices (Dynamic programming).

Architecture

Placeholder diagram for a typical problem-solving pipeline:

architecture

graph LR Problem --> Model Model --> Structure Structure --> Algorithm Algorithm --> Complexity

Key Concepts

Pattern recognition Most interview problems are variations of a small set of templates. The goal is not memorizing every problem, but mapping unknown tasks to known structures and invariants.
Complexity discipline State O(·) time and space for your approach before coding; adjust the approach if bounds fail the stated constraints.

Code Examples

def sum_first_n(nums: list[int], n: int) -> int:
    """O(n) time if n ~ len(nums); O(1) extra space."""
    total = 0
    for i in range(min(n, len(nums))):
        total += nums[i]
    return total

function two_pointer_sorted(arr):
  left = 0, right = len(arr) - 1
  while left < right:
    if arr[left] + arr[right] == target: return (left, right)
    elif sum too small: left += 1
    else: right -= 1

Interview Questions

How do you choose between a hash map and a tree-based map?

Prefer hash maps when you need expected O(1) lookups and either have a good hash for keys or can tolerate rare worst-case behavior. Prefer balanced trees when you need ordered traversal, range queries, or deterministic worst-case performance.

What is amortized analysis and where does it show up?

Amortized analysis averages the cost of a sequence of operations. Classic examples include dynamic array resizing and disjoint-set union optimizations.

Practice Problems

  • Arrays: two-sum variants, sliding window maximum, trapping rain water
  • Graphs: number of islands, course schedule (cycle detection)
  • DP: longest increasing subsequence, coin change, edit distance

Resources

  • CLRS — canonical algorithms reference
  • VisuAlgo — interactive visualizations
  • LeetCode — timed practice with discussion threads