Longest Increasing Subsequence in JavaScript

"use strict";
// Longest Increasing Subsequence in JavaScript
//
// PURPOSE
// Patience-style tail tracking finds the length of a longest strictly increasing subsequence
// using binary search. A subsequence may skip elements while preserving order.
//
// METHOD
// Keep the smallest possible tail for each subsequence length. Lower-bound search finds the
// first tail at least as large as the next value. Replace that tail or extend the length.
// Strict increase means equal values replace rather than extend.
//
// COMPLEXITY
// O(n log n) time and O(n) auxiliary space.
//
// CONTRACT
// Returns the length only. Equal values do not extend a strictly increasing subsequence.
// Empty input returns 0.
// 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: 4.
// 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 lis_length(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let tails = new Int32Array(alg_size(alg_add(n, 1)));
    let length = 0;
    let i = 0;
    let low = 0;
    let high = 0;
    let mid = 0;
    while ((i < n)) {
        low = 0;
        high = length;
        while ((low < high)) {
            mid = alg_add(low, Math.floor(alg_sub(high, low) / 2));
            if ((tails[mid] < a[i])) {
                low = alg_add(mid, 1);
            } else {
                high = mid;
            }
        }
        tails[low] = a[i];
        if ((low == length)) {
            length = alg_add(length, 1);
        }
        i = alg_add(i, 1);
    }
    return length;
}

let a = new Int32Array([10, 9, 2, 5, 3, 7, 101, 18]);
let result = lis_length(a);
console.log(result);