Two pointers maximize the area between a pair of height bars..
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 | "use strict"; // Container With Most Water in JavaScript // // PURPOSE // Two pointers maximize the area between a pair of height bars. // // METHOD // Evaluate width times the smaller height. Move the smaller-height endpoint inward: // retaining it with a shorter width cannot improve the area. // // COMPLEXITY // O(n) time, O(1) auxiliary space. // // CONTRACT // Nonnegative heights. Areas must fit signed 32-bit. Fewer than two bars 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: 49. // 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 max_container(a) { alg_require(a instanceof Int32Array); let n = a.length; alg_require(((n >= 0) && (n <= 1000000))); alg_require((a.length == n)); for (let alg_i = 0; alg_i < a.length; alg_i++) { let alg_value = a[alg_i]; alg_require((alg_value >= 0)); } let left = 0; let right = alg_sub(n, 1); let best = 0; while ((left < right)) { best = Math.max(best, alg_mul(alg_sub(right, left), Math.min(a[left], a[right]))); if ((a[left] <= a[right])) { left = alg_add(left, 1); } else { right = alg_sub(right, 1); } } return best; } let a = new Int32Array([1, 8, 6, 2, 5, 4, 8, 3, 7]); let result = max_container(a); console.log(result); |