Algorithms: Array Techniques

"use strict";
// Two Pointer Pair Sum in JavaScript
//
// PURPOSE
// Two pointers find whether two distinct positions in a sorted array sum to a target. Sorted
// order tells which pointer can improve the sum.
//
// METHOD
// Compare the sum at the two ends. Increase the left pointer when the sum is too small, or
// decrease the right pointer when too large. Each move safely eliminates one position.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space.
//
// CONTRACT
// Input must be sorted ascending. Returns 1 if a pair of distinct indices exists, otherwise
// 0. Pair sums 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: 1.
// 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 pair_sum(a, target) {
    alg_require(a instanceof Int32Array);
    alg_require(Number.isInteger(target) && target >= -2147483648 && target <= 2147483647);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let left = 0;
    let right = alg_sub(n, 1);
    let total = 0;
    while ((left < right)) {
        total = alg_add(a[left], a[right]);
        if ((total == target)) {
            return 1;
        }
        if ((total < target)) {
            left = alg_add(left, 1);
        } else {
            right = alg_sub(right, 1);
        }
    }
    return 0;
}

let a = new Int32Array([1, 2, 4, 7]);
let target = 9;
let result = pair_sum(a, target);
console.log(result);

// Two Pointer Pair Sum in Java
//
// PURPOSE
// Two pointers find whether two distinct positions in a sorted array sum to a target. Sorted
// order tells which pointer can improve the sum.
//
// METHOD
// Compare the sum at the two ends. Increase the left pointer when the sum is too small, or
// decrease the right pointer when too large. Each move safely eliminates one position.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space.
//
// CONTRACT
// Input must be sorted ascending. Returns 1 if a pair of distinct indices exists, otherwise
// 0. Pair sums 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 1.
// 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 pair_sum(int[] a, int target) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        int left = 0;
        int right = Math.subtractExact(n, 1);
        int total = 0;
        while ((left < right)) {
            total = Math.addExact(a[left], a[right]);
            if ((total == target)) {
                return 1;
            }
            if ((total < target)) {
                left = Math.addExact(left, 1);
            } else {
                right = Math.subtractExact(right, 1);
            }
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 2, 4, 7};
        int target = 9;
        int result = pair_sum(a, target);
        System.out.println(result);
    }
}

<?php
declare(strict_types=1);
// Fixed Sliding Window Maximum Sum in PHP
//
// 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
// 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: 9.
// 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 sliding_window_sum(array $a, int $k): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    alg_require((($k >= 1) && ($k <= $n)));
    $total = 0;
    $i = 0;
    while (($i < $k)) {
        $total = alg_add($total, $a[$i]);
        $i = alg_add($i, 1);
    }
    $best = $total;
    while (($i < $n)) {
        $total = alg_add($total, alg_sub($a[$i], $a[alg_sub($i, $k)]));
        $best = max($best, $total);
        $i = alg_add($i, 1);
    }
    return $best;
}

$a = [2, 1, 5, 1, 3, 2];
$k = 3;
$result = sliding_window_sum($a, $k);
echo $result, PHP_EOL;

using System;
// Fixed Sliding Window Maximum Sum in C#
//
// 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
// 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: 9.
// 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 sliding_window_sum(ReadOnlySpan<int> a, int k) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require(((k >= 1) && (k <= n)));
            int total = 0;
            int i = 0;
            while ((i < k)) {
                total = (total + a[i]);
                i = (i + 1);
            }
            int best = total;
            while ((i < n)) {
                total = (total + (a[i] - a[(i - k)]));
                best = Math.Max(best, total);
                i = (i + 1);
            }
            return best;
        }
    }

    static void Main() {
        int[] a = new int[] {2, 1, 5, 1, 3, 2};
        int k = 3;
        int result = sliding_window_sum(a, k);
        Console.WriteLine(result);
    }
}

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Fixed Sliding Window Maximum Sum in C++
//
// 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
// 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: 9.
// 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 sliding_window_sum(const std::vector<int>& a, int k) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    alg_require(((k >= 1) && (k <= n)));
    int total = 0;
    int i = 0;
    while ((i < k)) {
        total = alg_add(total, a[i]);
        i = alg_add(i, 1);
    }
    int best = total;
    while ((i < n)) {
        total = alg_add(total, alg_sub(a[i], a[alg_sub(i, k)]));
        best = alg_max(best, total);
        i = alg_add(i, 1);
    }
    return best;
}

int main(void) {
    std::vector<int> a = {2, 1, 5, 1, 3, 2};
    int k = 3;
    int result = sliding_window_sum(a, k);
    printf("%d\n", result);
    return 0;
}