Algorithms: Array Techniques

using System;
// Container With Most Water in C#
//
// 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
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 49.
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int max_container(ReadOnlySpan<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            for (int alg_i = 0; alg_i < a.Length; alg_i++) {
                int alg_value = a[alg_i];
                alg_require((alg_value >= 0));
            }
            int left = 0;
            int right = (n - 1);
            int best = 0;
            while ((left < right)) {
                best = Math.Max(best, ((right - left) * Math.Min(a[left], a[right])));
                if ((a[left] <= a[right])) {
                    left = (left + 1);
                } else {
                    right = (right - 1);
                }
            }
            return best;
        }
    }

    static void Main() {
        int[] a = new int[] {1, 8, 6, 2, 5, 4, 8, 3, 7};
        int result = max_container(a);
        Console.WriteLine(result);
    }
}

<?php
declare(strict_types=1);
// Container With Most Water in PHP
//
// 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
// PHP 8.1+ on a 64-bit runtime: packed arrays, strict scalar types, read-only inputs by
// value using copy-on-write, references only for outputs, and checked 32-bit arithmetic.
// Invalid input and overflow throw exceptions. PHP arrays have higher overhead than native
// packed buffers in C/Java.
//
// EXAMPLE
// Expected return: 49.
// Run: php example.php
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(bool $valid): void { if (!$valid) throw new InvalidArgumentException("invalid algorithm input"); }
function alg_checked(int|float $v): int { if ($v < -2147483648 || $v > 2147483647 || floor($v) != $v) throw new OverflowException("32-bit result overflow"); return (int)$v; }
function alg_add(int $a,int $b): int { return alg_checked($a+$b); }
function alg_sub(int $a,int $b): int { return alg_checked($a-$b); }
function alg_mul(int $a,int $b): int { return alg_checked($a*$b); }
function alg_size(int $n): int { alg_require($n>=0 && $n<=4000000); return $n; }

function max_container(array $a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    for ($alg_i = 0; $alg_i < count($a); $alg_i++) {
        $alg_value = $a[$alg_i];
        alg_require(($alg_value >= 0));
    }
    $left = 0;
    $right = alg_sub($n, 1);
    $best = 0;
    while (($left < $right)) {
        $best = max($best, alg_mul(alg_sub($right, $left), min($a[$left], $a[$right])));
        if (($a[$left] <= $a[$right])) {
            $left = alg_add($left, 1);
        } else {
            $right = alg_sub($right, 1);
        }
    }
    return $best;
}

$a = [1, 8, 6, 2, 5, 4, 8, 3, 7];
$result = max_container($a);
echo $result, PHP_EOL;

// Trapping Rain Water in Java
//
// PURPOSE
// Two boundary maxima determine trapped water above each bar.
//
// METHOD
// Process the side with the smaller boundary maximum, because the opposite side already
// provides a sufficiently high boundary. Accumulate that side's maximum minus its bar
// height.
//
// COMPLEXITY
// O(n) time, O(1) auxiliary space.
//
// CONTRACT
// Heights are nonnegative. Total volume must fit signed 32-bit.
// 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 6.
// Run: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class AlgorithmExample {
    static void alg_require(boolean valid) { if (!valid) throw new IllegalArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int trapped_water(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        for (int alg_i = 0; alg_i < a.length; alg_i++) {
            int alg_value = a[alg_i];
            alg_require((alg_value >= 0));
        }
        int left = 0;
        int right = Math.subtractExact(n, 1);
        int left_max = 0;
        int right_max = 0;
        int total = 0;
        while ((left <= right)) {
            if ((left_max <= right_max)) {
                left_max = Math.max(left_max, a[left]);
                total = Math.addExact(total, Math.subtractExact(left_max, a[left]));
                left = Math.addExact(left, 1);
            } else {
                right_max = Math.max(right_max, a[right]);
                total = Math.addExact(total, Math.subtractExact(right_max, a[right]));
                right = Math.subtractExact(right, 1);
            }
        }
        return total;
    }

    public static void main(String[] args) {
        int[] a = new int[] {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};
        int result = trapped_water(a);
        System.out.println(result);
    }
}

"use strict";
// Trapping Rain Water in JavaScript
//
// PURPOSE
// Two boundary maxima determine trapped water above each bar.
//
// METHOD
// Process the side with the smaller boundary maximum, because the opposite side already
// provides a sufficiently high boundary. Accumulate that side's maximum minus its bar
// height.
//
// COMPLEXITY
// O(n) time, O(1) auxiliary space.
//
// CONTRACT
// Heights are nonnegative. Total volume must fit signed 32-bit.
// 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: 6.
// 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 trapped_water(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 left_max = 0;
    let right_max = 0;
    let total = 0;
    while ((left <= right)) {
        if ((left_max <= right_max)) {
            left_max = Math.max(left_max, a[left]);
            total = alg_add(total, alg_sub(left_max, a[left]));
            left = alg_add(left, 1);
        } else {
            right_max = Math.max(right_max, a[right]);
            total = alg_add(total, alg_sub(right_max, a[right]));
            right = alg_sub(right, 1);
        }
    }
    return total;
}

let a = new Int32Array([0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]);
let result = trapped_water(a);
console.log(result);

from bisect import bisect_left

# Trapping Rain Water in Python
#
# PURPOSE
# Two boundary maxima determine trapped water above each bar.
#
# METHOD
# Process the side with the smaller boundary maximum, because the opposite side already
# provides a sufficiently high boundary. Accumulate that side's maximum minus its bar
# height.
#
# COMPLEXITY
# O(n) time, O(1) auxiliary space.
#
# CONTRACT
# Heights are nonnegative. Total volume must fit signed 32-bit.
# 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
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 6.
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def trapped_water(a: list[int]) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    for value in a:
        alg_require(value >= 0)
    left: int = 0
    right: int = n - 1
    left_max: int = 0
    right_max: int = 0
    total: int = 0
    while left <= right:
        if left_max <= right_max:
            left_max = max(left_max, a[left])
            total += left_max - a[left]
            left += 1
        else:
            right_max = max(right_max, a[right])
            total += right_max - a[right]
            right -= 1
    return total

a = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]
result = trapped_water(a)
print(result)