# Book Isle algorithm appendices: hand-trace each state with three invented inputs

Language: en
Canonical: [Book Isle algorithm appendices: hand-trace each state with three invented inputs](<https://allluckly.cn/en/guides/nasbook-appendix-algorithm-handtrace/>)
中文：[中文 HTML](<https://allluckly.cn/guides/nasbook-appendix-algorithm-handtrace/>)
English: [English HTML](<https://allluckly.cn/en/guides/nasbook-appendix-algorithm-handtrace/>)
Published: 2026-11-04T00:00:00+08:00
Modified: 2026-11-04T09:36:55+08:00
Author: Bison

Turn appendix steps into a checkable state log and hand-trace a maximum scan over 2, 5 and 3, distinguishing the book’s rules from your test.

English translation of the [Chinese original](<https://allluckly.cn/guides/nasbook-appendix-algorithm-handtrace/>), translated on 2026-11-04. Original publication dates, attribution, code and version notes are retained.

Understanding an algorithm appendix takes more than a note saying you understand. Read its instructions in Book Isle, then record each input, decision and state on paper or in an external log. The values 2, 5 and 3 are an invented teaching example, not data attributed to a real appendix. Book Isle does not execute the program or automatically prove its correctness; you perform the trace and checks manually.

## Read the actual appendix scope and assumptions

Choose a short algorithm explanation you are entitled to read and record the title, edition, appendix heading and exact location. Read its inputs, output and constraints in full. Distinguish pseudocode, prose explanation and examples; printed code is not an executable app feature. Revisit prior definitions before tracing dependent variables. This tutorial demonstrates finding a maximum in a nonempty number sequence. Use it as a comparison only if the actual text specifies that procedure. A sorting or other algorithm needs a different small example that follows its own rules, not this trace relabelled as the same process.

## Label the teaching input and intended output

Write the invented input in order as 2, 5, 3 and the target as returning the maximum value, not its position or a sorted sequence. Preserve the order instead of sorting to 2, 3, 5 and claiming to follow the original. Identify this as your own example; do not use quotation marks or a book-page attribution to make it look authored by the book. Use ordinary comparable numbers without missing, null or special values. Three items show both candidate replacement and retention. Keep this first task narrow before adding inputs whose extra rules could obscure the source of a discrepancy.

## Define initialisation and per-round record fields

Define the example’s rule: initialise the candidate from the first item, then compare each item from the second onward, replacing the candidate only for a greater value. Record candidate 2, next position 2 and remaining values 5 and 3. Initialisation is not a comparison against itself. Log round, current input, candidate before, condition result, candidate after and processed range in an external list; no algorithm-trace table is assumed in the reader. If the actual appendix initialises differently, follow its text. In particular, do not substitute zero as a universally valid initial maximum; negative inputs expose that error.

## Record decisions and unchanged states round by round

Round one reads the second item, 5: 5 is greater than candidate 2, so replace the candidate with 5 and mark the first two items processed. Round two reads 3: 3 is not greater than 5, so retain 5 and mark all three processed. Record this unchanged state; it explains why the output is not the last item, 3. Two comparisons for three inputs follows this example’s first-item initialisation and is not a rule for every loop. Check condition direction, input position and update order against the appendix at each row. A coincidentally correct final answer cannot validate an incorrect process.

## Check candidate meaning against the processed prefix

After each round, ask whether the candidate is the maximum of the processed prefix: 5 among 2 and 5, then 5 among 2, 5 and 3. This checks a finite hand trace, not correctness for every possible sequence. State termination: there is no fourth item, so output candidate 5 without reading another unknown value. A general proof requires separately studying the book’s invariant and termination argument; your small table is not that proof. Completion means explaining each replacement or retention from the record, not merely remembering the answer 5.

## Change one condition at a time in extra tests

In a separate copy, test −2, −5, −3. First-item initialisation should retain and return −2, revealing an incorrect zero initialisation. A separate 5, 5, 3 test explores equal maxima: a strict greater-than comparison retains value 5, but a task returning a position needs the book’s tie rule, which this tutorial does not define. An empty sequence violates the nonempty precondition; do not guess a zero return. Preserve each input and expectation separately instead of overwriting the first trace. These few tests do not eliminate every possible program defect.

## Keep source locators and trace provenance together

Use available notes to record the appendix locator, rule summary and external trace filename. Quote only necessary conditions where text selection works, and separately identify personal inputs and conclusions. For scans, record chapter and image page manually without inventing an exact text anchor. Leave and retrieve the original instructions from the record, checking initialisation and termination. Export important notes where supported and inspect them externally; keep book and trace separately because a note file is not the complete book. Label the record manual trace with a date. A later implementation is separate work; this reading record is not an app execution log.

## Find the earliest divergent row when answers disagree

If your result is not 5, locate the earliest candidate divergence and check reversed conditions, unconditional replacement or skipped inputs. If the result is right but the round count differs, inspect initialisation and processed ranges instead of approving the whole process from its output. Before disagreeing with the book’s example, compare its input and preconditions. Enlarge unclear symbols or consult the legitimate source rather than continuing from a guess. A finished record reconstructs input, rule, every state and stopping reason. Mark specific unresolved rows; the benefit is an explainable process, not an unverified answer supposedly produced by the app.

## Related tutorials and sources

[Read arguments in Book Isle: separate claims, evidence and inferential links](<https://allluckly.cn/en/guides/nasbook-claim-evidence-bridge/>), [Book Isle figure references: connect numbers, pages and reading notes](<https://allluckly.cn/en/guides/nasbook-figure-number-notes/>).

Sources checked on November 4, 2026: Book Isle 1.1.3, requiring iOS / iPadOS 15.6 or later. Capability scope follows the [official App Store description](<https://apps.apple.com/cn/app/id6766198898>) and [Apple public version lookup](<https://itunes.apple.com/lookup?id=6766198898&country=cn>). These are exercises and checks you can perform, without a claim of step-by-step physical-device testing or verification in every target environment. Example content is instructional; follow the controls in your installed version.