Algorithms by the Numbers: Counting Steps, Growth Rates, Binary Search, Sorting Comparisons, Hash Table Load & Caching
Understand algorithm efficiency without writing code: count loop steps, compare growth rates, trace binary search and a sorting pass, size hash tables and caches and choose an algorithm for a time budget, with every cell checked as you go.
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About this course
This course explains algorithm efficiency by counting instead of coding. You count the steps of nested and halving loops, fill growth tables for n log n, n² and 2ⁿ and chart where the curves cross. You compare linear and binary search, trace a binary search through a sorted list with INDEX, and follow one pass of a simple sort with MAX and MIN. Then you turn steps into run times on a fictional machine, find the largest input within one second with SQRT, LOG and MAXIFS, size hash tables by load factor, calculate cache hit rates and average access times, and choose the right algorithm for a time and memory budget.
Lessons
- Counting Steps: Single, Nested and Halving Loops Pro
- Growth Tables: n log n, n², 2ⁿ and Where the Curves Cross Pro
- Linear vs Binary Search: Worst-Case Comparisons and a Traced Search Pro
- Sorting Comparisons: n(n−1)/2 vs n · log₂ n and One Traced Pass Pro
- Time Budgets: Steps per Second, Run Times and the Largest n in One Second Pro
- Hash Tables: Load Factor, Expected Probes and Resize Thresholds Pro
- Caching: Hit Rates, Average Access Time and Cache Size Pro
- Dynamic Arrays & Amortised Cost, Capstone: Choose the Algorithm Pro