Fixed Sliding Window Maximum Sum in JavaScript

"use strict";
// Fixed Sliding Window Maximum Sum in JavaScript
//
// PURPOSE
// A fixed sliding window reuses the previous window sum rather than adding every window from
// scratch. This handles negative values as well as positive ones.
//
// METHOD
// Sum the first k entries. Advance one position by adding the entering value and subtracting
// the leaving value, keeping the largest total.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space.
//
// CONTRACT
// 1 <= k <= n. Returns the maximum sum over windows of exactly k elements. Totals must fit.
// 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: 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 sliding_window_sum(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 >= 1) && (k <= n)));
    let total = 0;
    let i = 0;
    while ((i < k)) {
        total = alg_add(total, a[i]);
        i = alg_add(i, 1);
    }
    let best = total;
    while ((i < n)) {
        total = alg_add(total, alg_sub(a[i], a[alg_sub(i, k)]));
        best = Math.max(best, total);
        i = alg_add(i, 1);
    }
    return best;
}

let a = new Int32Array([2, 1, 5, 1, 3, 2]);
let k = 3;
let result = sliding_window_sum(a, k);
console.log(result);