[FE] Complete Code Challenge Problems 1–3 DO NGUYEN TRONG (mytaekwondo@hotmail.com)

src/problem1/README.md

@@ -0,0 +1,189 @@
+# Problem 1 — Three pure functions with a separate audit layer
+
+## Design
+
+The implementation and audit responsibilities are deliberately separated:
+
+```text
+index.js  → three pure sum functions only
+audit.js  → calls the functions, builds independent proofs, and writes logs
+```
+
+`index.js` does not know about log files, hashes, manifests, callbacks, or the
+CLI. Each exported solution accepts exactly one argument: `n`.
+
+## Files
+
+```text
+src/problem1/
+├── index.js
+├── audit.js
+├── verify-audit.js
+├── stress-test.js
+├── run-stress.cmd
+├── README.md
+└── logs/
+```
+
+## The three functions in `index.js`
+
+### A. Closed-form arithmetic-series formula
+
+```javascript
+sum_to_n_a(n)
+```
+
+Uses `n(n + 1) / 2`, dividing the even factor before multiplication.
+
+```text
+Time:  O(1)
+Space: O(1)
+```
+
+### B. Fast matrix exponentiation
+
+```javascript
+sum_to_n_b(n)
+```
+
+Uses a fixed 3 × 3 transition matrix and exponentiation by squaring.
+
+```text
+Time:  O(log |n|)
+Space: O(1)
+```
+
+### C. Symmetric pairing loop
+
+```javascript
+sum_to_n_c(n)
+```
+
+Pairs the smallest and largest values. The actual implementation performs the
+loop so it remains computationally distinct from solution A.
+
+```text
+Time:  O(|n|)
+Space: O(1)
+```
+
+## Normal execution
+
+```javascript
+const {
+  sum_to_n_a,
+  sum_to_n_b,
+  sum_to_n_c,
+} = require("./index");
+
+console.log(sum_to_n_a(5)); // 15
+console.log(sum_to_n_b(5)); // 15
+console.log(sum_to_n_c(5)); // 15
+```
+
+Negative input follows this documented convention:
+
+```javascript
+sum_to_n_a(-4); // -10 = -1 + -2 + -3 + -4
+```
+
+## Separate audit function
+
+`audit.js` exports:
+
+```javascript
+auditAlgorithm({ key, n, algorithm, writeEvent })
+```
+
+For one algorithm it:
+
+1. calls the pure function from `index.js`;
+2. records the returned value;
+3. generates a separate mathematical proof inside `audit.js`;
+4. compares the implementation result with the proof result;
+5. sends structured events to the provided writer.
+
+The session-level helper is:
+
+```javascript
+runAudit({ n, selectedAlgorithm })
+```
+
+## Run an audit
+
+From `src/problem1`:
+
+```bat
+node audit.js 5 all
+```
+
+Or one implementation:
+
+```bat
+node audit.js 5 a
+node audit.js 5 b
+node audit.js 5 c
+```
+
+Generated evidence:
+
+```text
+logs\audit-....log
+logs\audit-....jsonl
+logs\audit-....manifest.json
+```
+
+The JSONL evidence uses a SHA-256 hash chain. Every event contains:
+
+- continuous `globalStep`;
+- one `auditId`;
+- `previousHash`;
+- `eventHash`;
+- timestamp;
+- algorithm;
+- action;
+- calculation data.
+
+## Verify an audit
+
+```bat
+node verify-audit.js logs\<manifest-file>.manifest.json
+```
+
+Expected result:
+
+```text
+Audit integrity: VALID
+```
+
+Changed, removed, reordered, duplicated, or truncated evidence is detected.
+
+## Run tests
+
+Recommended before commit:
+
+```bat
+node stress-test.js standard
+```
+
+Quick mode:
+
+```bat
+node stress-test.js smoke
+```
+
+The suite verifies, among other cases:
+
+- exact results against a BigInt oracle;
+- positive, zero, negative, and boundary inputs;
+- invalid input rejection;
+- all three functions expose one declared parameter;
+- audit instrumentation is owned by `audit.js` rather than `index.js`;
+- independent proof comparison;
+- audit CLI behavior;
+- file-system failures;
+- injected algorithm failures;
+- mutation sensitivity;
+- evidence tampering and truncation;
+- concurrent audit isolation;
+- performance and long-loop behavior.

src/problem1/STRESS-TEST.md

@@ -0,0 +1,78 @@
+# Problem 1 stress test
+
+Place these files in:
+
+```text
+D:\99\code-challenge\src\problem1\
+```
+
+## Standard run
+
+When the terminal is already in `src\problem1`:
+
+```bat
+node stress-test.js standard
+```
+
+Or:
+
+```bat
+run-stress.cmd standard
+```
+
+From the repository root:
+
+```bat
+node src\problem1\stress-test.js standard
+```
+
+## Modes
+
+```text
+smoke     Fast verification
+standard  Recommended before committing
+heavy     High-volume test
+```
+
+Examples:
+
+```bat
+node stress-test.js smoke
+node stress-test.js standard
+node stress-test.js heavy
+```
+
+Use a deterministic seed:
+
+```bat
+node stress-test.js standard 20260803
+```
+
+The same mode and seed produce the same random inputs.
+
+## Coverage
+
+The stress test checks:
+
+- edge cases and zero;
+- positive and negative integers;
+- exhaustive small ranges;
+- deterministic randomized inputs;
+- precision near `Number.MAX_SAFE_INTEGER`;
+- exact BigInt reference values;
+- agreement between implementations;
+- `S(-n) = -S(n)`;
+- `S(n) - S(n - 1) = n`;
+- invalid input rejection;
+- audit callback events from `index.js`;
+- integration with `audit.js`;
+- throughput and the long-running O(n) implementation.
+
+## Reports
+
+Reports are written to:
+
+```text
+src\problem1\logs\stress-test-....log
+src\problem1\logs\stress-test-....json
+```