Quickselect in JavaScript

"use strict";
// Quickselect in JavaScript
//
// PURPOSE
// Quickselect finds a zero-based order statistic without fully sorting the input.
//
// METHOD
// Partition around the middle-position pivot using a three-way partition. Retain only the
// side containing rank k, or return the pivot when k lies in the equal region.
//
// COMPLEXITY
// O(n) expected time for random input; O(n squared) worst case for this deterministic pivot.
// O(1) auxiliary space.
//
// CONTRACT
// 0 <= k < n. Mutates input. Returns the kth smallest value, counting duplicates.
// 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: 5.
// Expected a after call: [2, 2, 5, 7, 9].
// 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 quickselect(a, k) {
    alg_require(a instanceof Int32Array);
    alg_require(Number.isInteger(k) && k >= -2147483648 && k <= 2147483647);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    alg_require(((k >= 0) && (k < n)));
    let low = 0;
    let high = alg_sub(n, 1);
    let left = 0;
    let mid = 0;
    let right = 0;
    let pivot = 0;
    let temp = 0;
    while ((low <= high)) {
        pivot = a[alg_add(low, Math.floor(alg_sub(high, low) / 2))];
        left = low;
        mid = low;
        right = high;
        while ((mid <= right)) {
            if ((a[mid] < pivot)) {
                temp = a[left];
                a[left] = a[mid];
                a[mid] = temp;
                left = alg_add(left, 1);
                mid = alg_add(mid, 1);
            } else {
                if ((a[mid] > pivot)) {
                    temp = a[mid];
                    a[mid] = a[right];
                    a[right] = temp;
                    right = alg_sub(right, 1);
                } else {
                    mid = alg_add(mid, 1);
                }
            }
        }
        if ((k < left)) {
            high = alg_sub(left, 1);
        } else {
            if ((k > right)) {
                low = alg_add(right, 1);
            } else {
                return pivot;
            }
        }
    }
    return alg_sub(0, 1);
}

let a = new Int32Array([7, 2, 9, 2, 5]);
let k = 2;
let result = quickselect(a, k);
console.log(result);
// Expected a: [2, 2, 5, 7, 9]
console.log(Array.from(a));