Learning Algorithms from Scratch

Lesson Promise

By the end of this lesson, you will understand what an algorithm actually is, why arrays give you O(1) indexing, and how a linear search or array insertion really executes in memory. No prior knowledge required.

Narration Draft

Part 1 — What Is an Algorithm? (2:00) An algorithm is a precise, step-by-step procedure for solving a problem. Think of a recipe: given ingredients (input), follow steps, get a dish (output). We look at pseudocode as a way to describe algorithms without worrying about syntax.

Part 2 — Arrays and Memory (4:00) An array stores elements contiguously. The CPU computes address = base + index × size in one cycle — that is why indexing is O(1). A cache line fetches 16 adjacent integers at once, which is why sequential access is fast. Visual: draw memory from 0x1000 to 0x1020, show how array[3] is computed.

Part 3 — Tracing a Linear Search (3:00) Walk through searching for 7 in [3, 1, 4, 1, 5, 9, 2, 6, 5, 3]. Show each element being read, each comparison, and why the worst case is O(n).

Part 4 — Tracing an Array Insertion (3:00) Show inserting 35 at index 2 in a full array. First resize (5→10), then shift three elements right, then write the new value. Contrast with linked list insertion where only two pointers change.

Visual Sequence

1. "What is an algorithm?" text + recipe analogy
2. Array memory layout: contiguous cells at 0x1000, 0x1004, 0x108
3. Cache line animation: one fetch loads 16 cells
4. Linear search: highlight each cell, show comparison result
5. Array insertion: show resize → shift → write
6. Side-by-side: array vs linked list memory comparison

Companion Material

• Article: What Is an Algorithm?
• Article: Arrays and Memory
• Diagram: Array vs Linked List Layout
• Trace: Linear Search
• Trace: Array Insertion
• Practice: Implement Binary Search