Counting Sort in JavaScript

"use strict";
// Counting Sort in JavaScript
//
// PURPOSE
// Counting sort counts each possible key instead of comparing pairs. It is efficient when
// nonnegative integer keys occupy a small range.
//
// METHOD
// Count occurrences in a frequency array, then write each key the recorded number of times.
// The output prefix is sorted throughout reconstruction.
//
// COMPLEXITY
// O(n + k) time and O(k) auxiliary space, where k = maximum + 1. This key-only version does
// not demonstrate stable sorting of records.
//
// CONTRACT
// All n values must be between 0 and maximum inclusive. Sorts in place and returns 0. A huge
// maximum makes this approach unsuitable.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// Node.js 18+: Int32Array inputs and workspaces provide compact integer storage. Automatic
// lengths and checked arithmetic reject values outside signed 32-bit. Invalid inputs or
// overflow throw RangeError.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [1, 1, 3, 5].
// Run: node example.js
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(valid) { if (!valid) throw new RangeError("invalid algorithm input"); }
function alg_checked(v) { if (!Number.isInteger(v) || v < -2147483648 || v > 2147483647) throw new RangeError("32-bit result overflow"); return v; }
function alg_add(a,b) { return alg_checked(a+b); }
function alg_sub(a,b) { return alg_checked(a-b); }
function alg_mul(a,b) { return alg_checked(a*b); }
function alg_size(n) { alg_require(Number.isInteger(n) && n>=0 && n<=4000000); return n; }

function counting_sort(a, maximum) {
    alg_require(a instanceof Int32Array);
    alg_require(Number.isInteger(maximum) && maximum >= -2147483648 && maximum <= 2147483647);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    alg_require(((maximum >= 0) && (maximum <= 1000000)));
    for (let alg_i = 0; alg_i < a.length; alg_i++) {
        let alg_value = a[alg_i];
        alg_require(((alg_value >= 0) && (alg_value <= maximum)));
    }
    let counts = new Int32Array(alg_size(alg_add(maximum, 1)));
    let i = 0;
    let value = 0;
    let out = 0;
    while ((i < n)) {
        counts[a[i]] = alg_add(counts[a[i]], 1);
        i = alg_add(i, 1);
    }
    while ((value <= maximum)) {
        while ((counts[value] > 0)) {
            a[out] = value;
            out = alg_add(out, 1);
            counts[value] = alg_sub(counts[value], 1);
        }
        value = alg_add(value, 1);
    }
    return 0;
}

let a = new Int32Array([5, 1, 3, 1]);
let maximum = 5;
let result = counting_sort(a, maximum);
console.log(result);
console.log(a);
// Expected a: [1, 1, 3, 5]