Personal Reflections on Algorithms, Data Structures, and Complexity

Chapter 1: Algorithm Overview

1. Algorithms

What is an algorithm? The book uses the example of summing 1+2+3+…+10000 and asks how you would compute it—by adding one by one or by using a trick. The author interprets an algorithm simply as a method of calculation.

In computer programming, algorithms are applied to operations such as computation, searching, sorting, optimal decision‑making, routing, and interview problems. The key is not just getting the correct result, but doing it faster and more concisely.

Efficiency matters: two solutions may produce the same answer, but the one that uses fewer steps or less time is considered better.

2. Data Structures

Data is what we store; a structure is how we store it. Efficient storage and retrieval require organized structures rather than random placement.

Common data structures include linear structures (arrays, linked lists, stacks, queues), trees, graphs, and many others such as hash tables and bitmaps.

Linear structures are simple sequences; trees have hierarchical branches; graphs capture relationships between items.

3. Complexity

Both algorithms and data structures are evaluated by their efficiency—how fast they run and how much memory they consume.

3.1 Time Complexity

Time complexity is expressed with Big‑O notation (e.g., O(n), O(log n), O(2ⁿ)). It abstracts the growth rate of an algorithm’s running time as the input size increases.

Example: eating a 10 cm bread at 1 cm per 3 minutes takes 30 minutes; for a length n, the time is 3n minutes, giving a linear time complexity O(n).

The author emphasizes that even with faster hardware, understanding time complexity remains important because algorithmic growth can dominate performance.

3.2 Space Complexity

Space complexity, also expressed with Big‑O, measures the amount of extra memory an algorithm requires during execution.

Example: finding two duplicate numbers in a list can be done by scanning each element (high space/time) or by using a dictionary to record occurrences, which reduces both.

Space complexity categories include constant, linear, quadratic, and recursive space usage.

Chapter 2: Basics of Data Structures

1. Arrays

Arrays are ordered collections where each element has an index. Operations such as insertion, deletion, and lookup have different time and space costs.

2. Linked Lists

Linked lists are non‑contiguous structures where each node points to the next (and optionally the previous) node, allowing flexible insertion and deletion.

2.1 Singly Linked List

Structure: A → B → C → D → NULL. Each node stores data and a pointer to the next node.

2.2 Doubly Linked List

Structure: NULL ←→ A ↔ B ↔ C ↔ D → NULL. Each node has pointers to both the next and previous nodes, enabling traversal in both directions.

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