feat(js): m01 util and m02 model with tests, fixtures, purity audit

Co-Authored-By: Claude Sonnet 5.5 <[email protected]>

js/solutions/util.js

@@ -0,0 +1,29 @@
+// m01 util: small helpers used by every later module.
+
+/** `range(n)` is `[0, 1, ..., n-1]`; `range(0)` is `[]`. */
+export const range = (n) => Array.from({ length: n }, (_, i) => i)
+
+/** `xs` without its last element; an empty list stays empty. Never mutates `xs`. */
+export const dropLast = (xs) => xs.slice(0, -1)
+
+/** True if some element `x` of `xs` satisfies `eq(x, p)`. `eq` lets callers compare structurally (e.g. `pointEquals`). */
+export const contains = (xs, p, eq) => xs.some((x) => eq(x, p))
+
+/** `pipe(x, f, g)` is `g(f(x))`: thread a value through functions left to right. */
+export const pipe = (x, ...fns) => fns.reduce((acc, f) => f(acc), x)
+
+/** `compose(f, g)(x)` is `f(g(x))`: functions applied right to left. */
+export const compose = (...fns) => (x) => fns.reduceRight((acc, f) => f(acc), x)
+
+/**
+ * Freeze `obj` and everything reachable from it, then return it.
+ * Freezing is the one deliberate "mutation" here: it makes later accidental mutation throw.
+ */
+export const deepFreeze = (obj) => {
+  Object.freeze(obj)
+  // Freezing before recursing means cyclic structures stop at the already-frozen node.
+  Object.values(obj).forEach((v) => {
+    if (v !== null && typeof v === 'object' && !Object.isFrozen(v)) deepFreeze(v)
+  })
+  return obj
+}