Fix correctness bugs found in a full-codebase audit

[moshejs]

Summary

A systematic audit of the repository (every claimed bug was verified by executing a concrete failing input before fixing) uncovered a number of correctness bugs, wrong documentation claims, and a few gaps. This PR fixes them, adds 54 regression tests, and keeps the full suite green: 179 suites / 641 tests pass, ESLint clean.

Data structure fixes

• AVL tree — four defects: rotateLeftLeft/rotateRightRight always attached the rotated-up node to a fixed side of the parent, losing whole subtrees when the unbalanced node sat on the other side (repro: insert 50, 30, 70, 65, 60 → node 30 vanished); all rotations corrupted parent pointers by attaching a transferred child before detaching it (setLeft/setRight detach logic then nulled the fresh parent reference); balance() ignored the zero-balance-factor child case that removals produce; and remove() only balanced the root once instead of retracing from the deepest affected node. A 200-operation randomized insert/remove invariant test now guards all of this.
• BinaryTreeNode.replaceChild never updated the promoted child's parent pointer, breaking parent chains after every one-child BST removal.
• BST remove unconditionally nulled the parent pointer of nodes that stayed in the tree (two-children case) and erased an empty root with undefined while insert checks for null, so a re-used tree grew a phantom root.
• Heap.remove used !parentItem to mean "no parent", so parent values of 0/''/false heapified in the wrong direction — PriorityQueue (default priority 0) was the common victim.
• LinkedList.insert at index == length linked the node after the tail without updating tail; the next append silently dropped it.
• RedBlackTree repainted the existing node red when inserting a duplicate value, breaking the red-red invariant.
• MinHeapAdhoc/MaxHeapAdhoc crashed on any non-empty constructor array (heap.forEach(this.add) loses this).
• LRUCache / HashTable misbehaved with keys inherited from Object.prototype ('constructor', '__proto__') — both registries now use prototype-less objects.
• SegmentTree crashed on an empty input array (log2(0) → array length −1).

Graph algorithm fixes

• articulationPoints, graphBridges, detectUndirectedCycle only examined the first connected component.
• eulerianPath crashed on valid inputs (bridge detection ran from a vertex Fleury had already isolated) and on disconnected even-degree graphs; it now validates connectivity and rejects directed graphs explicitly.
• bfTravellingSalesman never counted the closing edge's weight and accepted "tours" that skipped vertices.
• floydWarshall mixed two conventions in nextVertices (start vertex for direct edges, middle vertex on relaxation), making path reconstruction impossible; now uses the standard successor convention, with a path-reconstruction test.
• bellmanFord silently returned finite distances for graphs with negative cycles; it now throws after the standard extra relaxation pass.
• Graph.addEdge re-attached edge objects already present in a vertex's edge list, so building an MST via Kruskal/Prim corrupted the input graph's vertex degrees.
• Default BFS/DFS allowTraversal never marked the start vertex seen, so a directed cycle re-entered it (A→B→C→A visited A twice).
• stronglyConnectedComponents left the caller's graph permanently reversed; prim now throws on disconnected graphs instead of silently returning a partial tree.

Math / ML fixes

• Inverse FFT applied numeric /= to ComplexNumber objects → NaN for every signal; the test helper was NaN-blind (Math.abs(NaN) > delta is false) and is fixed too. Forward/inverse FFT kernels were also swapped relative to the standard convention and to discreteFourierTransform.js in the same folder.
• kMeans produced NaN centroids for empty clusters and returned cluster -1 for every point; euclideanDistance rounded to 2 decimals (toFixed(2)), destroying kNN tie-breaking.
• Infinite loops fixed: bitLength(2**30) (31-bit << wrap), fibonacciNth(0) / fibonacci(0), squareRoot(2, 17) (Newton's iteration 2-cycles between adjacent doubles), and fastPowering with negative exponents — which are now supported (2^-3 → 0.125).
• bitsToFloat now decodes IEEE 754 zeros, subnormals, and ±Infinity/NaN (previously the all-zero bit pattern decoded to 2⁻¹⁵, i.e. zero was unrepresentable).
• isPowerOfTwo(0) returned true; classicPolynome mutated the caller's coefficients array; weightedRandom could return a zero-weight item when Math.random() hit exactly 0.

Sorting / search / sets / string / crypto fixes

• interpolationSearch hung forever when the seek value was above the array maximum or between elements of non-uniform data.
• 0/1 knapsack traceback was broken (single item {v:5, w:2}, limit 3 → empty selection, value 0); unbounded knapsack pushed items with zero possible quantity, exceeding the weight limit.
• RadixSort placed shorter strings after 'z' instead of before 'a' (['b','ba'] → ['ba','b']) and mangled negative integers (now handled); BucketSort delegated buckets to RadixSort, which does zero passes on floats — buckets are now comparison-sorted.
• rabinKarp/PolynomialHash.roll indexed by UTF-16 code units against a code-point-based hash(), so any astral symbol in the window corrupted every subsequent rolling hash; the long-standing commented-out @TODO: Provide Unicode support test is now enabled and passing.
• zAlgorithm lost matches when the text contained the internal '$' separator (zAlgorithm('a$a', 'a') → [2] instead of [0, 2]).
• railFenceCipher dropped characters on encode and threw on decode with a single rail; hillCipher encrypted lowercase input inconsistently with uppercase ('act' ≠ 'ACT').
• hanoiTower(0) and both permutation generators recursed infinitely on empty input; dpTopDownJumpGame copied its memo table on every call (and wrote the seed to index −1), so the claimed memoization never happened; validParentheses('') returned false, contradicting the README's own vacuous-truth definition.

Documentation corrections (English READMEs)

Wrong Big-O claims (segment tree build is O(n), BST table now notes the unbalanced worst case, Z-algorithm space is O(|W|+|T|), recursive-staircase brute force is O(n) space), wrong math (polynomial-hash formula exponents, complex-number conjugate identity, square-matrix-rotation described a reflection order that yields a counterclockwise rotation), inverted pseudocode conditions (tree BFS, BST findMin/findMax preconditions), an inverted k-means stopping condition, and a few dozen grammar/typo fixes.

Additions

• Extended Euclidean algorithm (extendedEuclideanAlgorithm.js) with Bézout coefficients — the euclidean-algorithm README already discussed the identity with nothing computing it.
• Deque row in the main README complexity table; missing DP section in the best-time-to-buy-sell-stocks README.
• Honest notes where implementations differ from cheat-sheet values (this repo's heap sort uses O(n) memory; DisjointSet.js union is linear vs. the inverse-Ackermann DisjointSetAdhoc.js).

Notes for reviewers

• Two existing tests encoded buggy behavior and were deliberately updated: floydWarshall.test.js (asserted the inconsistent nextVertices values) and validParentheses.test.js (asserted isValid('') === false).
• Two design limitations were documented rather than redesigned: PriorityQueue keys priorities by item value (duplicates share one priority), and Kruskal/Prim MSTs share vertex objects with the source graph (the degree-corruption side effect is fixed here; full isolation would change the API).

🤖 Generated with Claude Code

[daltino]

DECISION: APPROVE

This PR focuses on fixing accuracy issues identified in various files, including updates to comments, documentation, and test cases to ensure correctness and clarity. The changes align well with the repository's contribution guidelines, maintaining the existing format and including tests for updates such as the rail fence cipher edge case. The added details improve clarity, particularly around algorithm behavior and performance.