Step Counter Simulator

Teach the same idea without “math mode”: run a mini-debugger that counts loop iterations and recursive calls.

Tips: Enter step · Space auto · R reset

Learning goal Loops: count repetitions Recursion: count calls + work per call Big-O: dominant growth

This page shows a trace (what runs), a stack view (for recursion), and a line hit heatmap (which statements dominate).

Pick an example

Big-O: —

Scenario

Input size n

The simulator limits trace length for huge runs and uses sampling when needed.

Counters

Total steps

Calls / iterations

Trace status

—

What to say while teaching

Heatmap shows which line dominates.
Loops dominate by repetition (hits explode).
Recursion dominates by #calls × local work.
Base case stops recursion — that sets the depth.

Code view + line hits

line hit heatmap updates while stepping

Line-hit Heatmap (dominance)

The line with the highest hit count usually explains the Big-O.

Execution trace

latest events

Trace log

Call stack (recursion)

empty for loops

How this teaches “recurrence vs loops” without math

Loops

The same line runs again and again. Big-O is the growth of “how many times the dominant line runs”.

Independent nested loops → hits multiply.
Dependent nested loops → hits form a summation (triangle).
Doubling/halving updates → logarithmic hits.

Recursion

Each call may create more calls (branching) and does some work (local cost). Total time is “number of calls × work per call” (plus shape effects).

Binary search: one call, size halves → shallow stack.
Merge sort: two calls, size halves + merge work → many calls but balanced.
Fibonacci: branching + slow shrink → explosion in call count.

Best classroom trick

Ask: “Which line got the most hits?” That line is the reason for Big-O.

Ideas to extend this page

Add a “Mystery Code” mode: students guess Big-O, then reveal heatmap proof.
Add a “Compare 2 algorithms” race: show step counters side-by-side.
Add “cost model”: toggle counts for comparisons vs assignments vs array access.
Add “sampling indicator”: show when trace is sampled to stay fast.

Index link snippet

<a href="10_step_counter_simulator.html" class="card-link">
  Step Counter Simulator (Loops vs Recursion)
</a>