Algorithms with State · Lesson 16 of 30 · about 12 minutes

Factorial and Loop Invariants

Use a multiplicative accumulator and explain why 0! is 1.

01 / Explain

Understand the idea

Factorial N! is the product N × (N − 1) × … × 1. A product accumulator starts at 1, the identity for multiplication. This also gives the mathematical result 0! = 1 when a zero-count loop performs no work.

Each iteration multiplies the total by the current factor, then decreases that factor. Keep the repeat count in its own register. The challenge uses small inputs because factorial grows quickly and the machine rejects unsafe integer results.

02 / Try

Watch it happen

Watch the total become 4, 12, 24, 24.

LOAD 4 R1
LOAD 1 R2
LOOP 4
LOAD R2
MUL R1
COPY R0 R2
LOAD R1
SUB 1
COPY R0 R1
RETURN
LOAD R2
PRINT
HALT

Use Step to follow one instruction at a time. You can change the example and replay it.

03 / Challenge

Make it work

Read N from 0 through 6 and print N!. Use a loop and a multiplication accumulator.

The checker runs your current editor program in a fresh machine for each of 3 test cases. It supplies inputs and seeded memory itself; the lab’s current output and memory do not decide your result.

INPUT
COPY R0 R1
COPY R0 R3
LOAD 1 R2
LOOP R3
  # Multiply by factor; decrease factor.
RETURN
LOAD R2
PRINT
HALT

Need a hint?

Start the total at 1 rather than zero.

Reveal a worked solution

Read the program, predict each instruction’s effect, then step through it in the lab.

INPUT
COPY R0 R1
COPY R0 R3
LOAD 1 R2
LOOP R3
LOAD R2
MUL R1
COPY R0 R2
LOAD R1
SUB 1
COPY R0 R1
RETURN
LOAD R2
PRINT
HALT

Emoji program

Type LOAD, ADD, or another opcode then Space to insert emoji. Ctrl/⌘ + Enter runs or pauses; Escape pauses; Ctrl/⌘ + ] indents. Tab moves focus. Labels use a colon. Jumps use zero-based instruction addresses.

INPUT
COPY R0 R1
COPY R0 R3
LOAD 1 R2
LOOP R3
  # Multiply by factor; decrease factor.
RETURN
LOAD R2
PRINT
HALT

Instruction map and breakpoints (0)

Breakpoints stop before an instruction. Run resumes past the stopped breakpoint once; Step executes it directly. Editing source clears old breakpoints and machine state.

Use Number

CPU registers

R0: 0
R1: 0
R2: 0
R3: 0
R4: 0
R5: 0
R6: 0
R7: 0

Program counter (PC): 0
Stack pointer (SP): 255
Flags: Zero: off · Negative: off · Overflow: off
Delay request: 0 ms

Stacks and loop frames

SP = 255 − data depth − call depth. The stack is separate from memory.

Data stack (bottom → top)

Empty

Call return addresses (bottom → top)

Empty

Loop frames

Empty

Output and input

Run a PRINT instruction to see output.

Queued input: Empty

Memory · 256 bytes · 0 nonzero

Each cell shows address:value. R = read this step; W = written this step. Select a cell to inspect or initialize it before execution. Use arrow keys to move, Home/End for the row, and Ctrl/⌘ + Home/End for the whole memory.

Execution trace · 0 entries

Recent entries below. Inspect any zero-based index to see complete detached before/after state.

Check your challenge

You can run this check any time. Every case must pass to record completion.

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