Algorithms: Array Techniques

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Trapping Rain Water in C
//
// 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
// C99: checked calloc/free workspace, const input pointers, explicit size_t lengths. Errors
// return INT_MIN with errno=EINVAL, ERANGE, or ENOMEM. Check errno before using a result.
// Input/output arrays must not alias. No variable-length stack arrays.
//
// EXAMPLE
// Expected return: 6.
// Run: gcc -std=c99 -O2 example.c -o example && ./example
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

static int alg_min(int a, int b) { return a < b ? a : b; }
static int alg_max(int a, int b) { return a > b ? a : b; }
static int alg_checked(int64_t v, int *error) {
    if (v < INT_MIN || v > INT_MAX) { *error = 1; return 0; }
    return (int)v;
}
static int alg_add(int a, int b, int *e) { return alg_checked((int64_t)a+b,e); }
static int alg_sub(int a, int b, int *e) { return alg_checked((int64_t)a-b,e); }
static int alg_mul(int a, int b, int *e) { return alg_checked((int64_t)a*b,e); }

int trapped_water(const int *a, size_t a_length) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    if (a_length > 1000000 || (a_length && !a)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    int n = (int)a_length;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((n >= 0) && (n <= 1000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((int)a_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    for (int alg_i = 0; alg_i < (int)a_length; alg_i++) {
        int alg_value = a[alg_i];
        if (!((alg_value >= 0))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    int left = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int right = alg_sub(n, 1, &alg_error);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int left_max = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int right_max = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int total = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (left <= right);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        int alg_condition_1 = (left_max <= right_max);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_1) {
            left_max = alg_max(left_max, a[left]);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            total = alg_add(total, alg_sub(left_max, a[left], &alg_error), &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            left = alg_add(left, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        } else {
            right_max = alg_max(right_max, a[right]);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            total = alg_add(total, alg_sub(right_max, a[right], &alg_error), &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            right = alg_sub(right, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
    }
    alg_result = total;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    return alg_result;
}

int main(void) {
    int a[] = {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};
    int result = trapped_water(a, 12);
    printf("%d\n", result);
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Trapping Rain Water in C++
//
// 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
// C++17: const vector references for inputs, mutable references for outputs, RAII workspace,
// standard lower_bound for LIS. Invalid inputs throw invalid_argument; overflow throws
// overflow_error; allocation failure propagates bad_alloc.
//
// EXAMPLE
// Expected return: 6.
// Run: g++ -std=c++17 -O2 example.cpp -o example && ./example
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

static int alg_min(int a, int b) { return a < b ? a : b; }
static int alg_max(int a, int b) { return a > b ? a : b; }
static void alg_require(bool valid) { if (!valid) throw std::invalid_argument("invalid algorithm input"); }
static int alg_checked(int64_t v) { if (v < INT32_MIN || v > INT32_MAX) throw std::overflow_error("32-bit result overflow"); return (int)v; }
static int alg_add(int a,int b) { return alg_checked((int64_t)a+b); }
static int alg_sub(int a,int b) { return alg_checked((int64_t)a-b); }
static int alg_mul(int a,int b) { return alg_checked((int64_t)a*b); }
static size_t alg_size(int n) { alg_require(n>=0 && n<=4000000); return (size_t)n; }

int trapped_water(const std::vector<int>& a) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    for (int alg_i = 0; alg_i < (int)a.size(); alg_i++) {
        int alg_value = a[alg_i];
        alg_require((alg_value >= 0));
    }
    int left = 0;
    int right = alg_sub(n, 1);
    int left_max = 0;
    int right_max = 0;
    int total = 0;
    while ((left <= right)) {
        if ((left_max <= right_max)) {
            left_max = alg_max(left_max, a[left]);
            total = alg_add(total, alg_sub(left_max, a[left]));
            left = alg_add(left, 1);
        } else {
            right_max = alg_max(right_max, a[right]);
            total = alg_add(total, alg_sub(right_max, a[right]));
            right = alg_sub(right, 1);
        }
    }
    return total;
}

int main(void) {
    std::vector<int> a = {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};
    int result = trapped_water(a);
    printf("%d\n", result);
    return 0;
}

using System;
// Trapping Rain Water in C#
//
// 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
// 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: 6.
// 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 trapped_water(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 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 = (total + (left_max - a[left]));
                    left = (left + 1);
                } else {
                    right_max = Math.Max(right_max, a[right]);
                    total = (total + (right_max - a[right]));
                    right = (right - 1);
                }
            }
            return total;
        }
    }

    static void Main() {
        int[] a = new int[] {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};
        int result = trapped_water(a);
        Console.WriteLine(result);
    }
}

<?php
declare(strict_types=1);
// Trapping Rain Water in PHP
//
// 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
// 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: 6.
// 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 trapped_water(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);
    $left_max = 0;
    $right_max = 0;
    $total = 0;
    while (($left <= $right)) {
        if (($left_max <= $right_max)) {
            $left_max = max($left_max, $a[$left]);
            $total = alg_add($total, alg_sub($left_max, $a[$left]));
            $left = alg_add($left, 1);
        } else {
            $right_max = max($right_max, $a[$right]);
            $total = alg_add($total, alg_sub($right_max, $a[$right]));
            $right = alg_sub($right, 1);
        }
    }
    return $total;
}

$a = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1];
$result = trapped_water($a);
echo $result, PHP_EOL;

// Monotonic Deque Sliding Maximum in Java
//
// PURPOSE
// A monotonic deque returns every fixed-window maximum in linear time.
//
// METHOD
// Keep candidate indices in decreasing value order. Discard expired indices from the front
// and dominated candidates from the back; the front is the current maximum.
//
// COMPLEXITY
// O(n) time; O(n) allocated index-buffer space in this linear-buffer implementation, with at
// most k live candidates.
//
// CONTRACT
// 1 <= k <= n. output has n-k+1 entries. Writes maximum values and returns output length.
// 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.
// Expected output after call: [3, 3, 5, 5, 6, 7].
// 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 sliding_maximum(int[] a, int k, int[] output) {
        java.util.Objects.requireNonNull(a, "a");
        java.util.Objects.requireNonNull(output, "output");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        alg_require((output.length == Math.addExact(Math.subtractExact(n, k), 1)));
        alg_require(((k >= 1) && (k <= n)));
        int[] queue = new int[alg_size(n)];
        int head = 0;
        int tail = 0;
        int i = 0;
        while ((i < n)) {
            while (((head < tail) && (queue[head] <= Math.subtractExact(i, k)))) {
                head = Math.addExact(head, 1);
            }
            while (((head < tail) && (a[queue[Math.subtractExact(tail, 1)]] <= a[i]))) {
                tail = Math.subtractExact(tail, 1);
            }
            queue[tail] = i;
            tail = Math.addExact(tail, 1);
            if ((i >= Math.subtractExact(k, 1))) {
                output[Math.addExact(Math.subtractExact(i, k), 1)] = a[queue[head]];
            }
            i = Math.addExact(i, 1);
        }
        return Math.addExact(Math.subtractExact(n, k), 1);
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 3, -1, -3, 5, 3, 6, 7};
        int k = 3;
        int[] output = new int[] {0, 0, 0, 0, 0, 0};
        int result = sliding_maximum(a, k, output);
        System.out.println(result);
        // Expected output: [3, 3, 5, 5, 6, 7]
        System.out.println(java.util.Arrays.toString(output));
    }
}