Algorithms: Array Techniques

// Boyer Moore Majority Vote in Java
//
// PURPOSE
// Majority vote cancels pairs of different values. If a value occurs more than half the
// time, it survives as the final candidate.
//
// METHOD
// Choose a new candidate whenever the balance is zero. Increment for matching values and
// decrement for different ones. Make a second pass to verify the candidate, since a majority
// need not exist.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space.
//
// CONTRACT
// Returns the INDEX of a verified majority value, or -1 if none exists. Returning an index
// avoids colliding with any valid integer value.
// 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: 0.
// 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 majority_index(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        int candidate = 0;
        int balance = 0;
        int i = 0;
        int count = 0;
        while ((i < n)) {
            if ((balance == 0)) {
                candidate = i;
            }
            if ((a[i] == a[candidate])) {
                balance = Math.addExact(balance, 1);
            } else {
                balance = Math.subtractExact(balance, 1);
            }
            i = Math.addExact(i, 1);
        }
        i = 0;
        while ((i < n)) {
            if ((a[i] == a[candidate])) {
                count = Math.addExact(count, 1);
            }
            i = Math.addExact(i, 1);
        }
        if ((count > (n / 2))) {
            return candidate;
        }
        return Math.negateExact(1);
    }

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

<?php
declare(strict_types=1);
// Dutch National Flag Partition in PHP
//
// PURPOSE
// Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
// grouping values around a pivot.
//
// METHOD
// Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
// advance past a one, or swap a two right and re-examine the incoming unknown value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space. Not stable.
//
// CONTRACT
// Every value must be 0, 1, or 2. Mutates the array into sorted order and 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: 0.
// Expected a after call: [0, 0, 1, 2, 2].
// 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 dutch_flag(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((($alg_value >= 0) && ($alg_value <= 2)));
    }
    $low = 0;
    $mid = 0;
    $high = alg_sub($n, 1);
    $temp = 0;
    while (($mid <= $high)) {
        if (($a[$mid] == 0)) {
            $temp = $a[$low];
            $a[$low] = $a[$mid];
            $a[$mid] = $temp;
            $low = alg_add($low, 1);
            $mid = alg_add($mid, 1);
        } else {
            if (($a[$mid] == 1)) {
                $mid = alg_add($mid, 1);
            } else {
                $temp = $a[$mid];
                $a[$mid] = $a[$high];
                $a[$high] = $temp;
                $high = alg_sub($high, 1);
            }
        }
    }
    return 0;
}

$a = [2, 0, 1, 2, 0];
$result = dutch_flag($a);
echo $result, PHP_EOL;
echo json_encode($a), PHP_EOL;
// Expected a: [0, 0, 1, 2, 2]

using System;
// Dutch National Flag Partition in C#
//
// PURPOSE
// Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
// grouping values around a pivot.
//
// METHOD
// Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
// advance past a one, or swap a two right and re-examine the incoming unknown value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space. Not stable.
//
// CONTRACT
// Every value must be 0, 1, or 2. Mutates the array into sorted order and 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: 0.
// Expected a after call: [0, 0, 1, 2, 2].
// 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 dutch_flag(Span<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) && (alg_value <= 2)));
            }
            int low = 0;
            int mid = 0;
            int high = (n - 1);
            int temp = 0;
            while ((mid <= high)) {
                if ((a[mid] == 0)) {
                    temp = a[low];
                    a[low] = a[mid];
                    a[mid] = temp;
                    low = (low + 1);
                    mid = (mid + 1);
                } else {
                    if ((a[mid] == 1)) {
                        mid = (mid + 1);
                    } else {
                        temp = a[mid];
                        a[mid] = a[high];
                        a[high] = temp;
                        high = (high - 1);
                    }
                }
            }
            return 0;
        }
    }

    static void Main() {
        int[] a = new int[] {2, 0, 1, 2, 0};
        int result = dutch_flag(a);
        Console.WriteLine(result);
        Console.WriteLine("[" + string.Join(", ", a) + "]");
        // Expected a: [0, 0, 1, 2, 2]
    }
}

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Dutch National Flag Partition in C++
//
// PURPOSE
// Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
// grouping values around a pivot.
//
// METHOD
// Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
// advance past a one, or swap a two right and re-examine the incoming unknown value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space. Not stable.
//
// CONTRACT
// Every value must be 0, 1, or 2. Mutates the array into sorted order and 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++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: 0.
// Expected a after call: [0, 0, 1, 2, 2].
// 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 dutch_flag(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) && (alg_value <= 2)));
    }
    int low = 0;
    int mid = 0;
    int high = alg_sub(n, 1);
    int temp = 0;
    while ((mid <= high)) {
        if ((a[mid] == 0)) {
            temp = a[low];
            a[low] = a[mid];
            a[mid] = temp;
            low = alg_add(low, 1);
            mid = alg_add(mid, 1);
        } else {
            if ((a[mid] == 1)) {
                mid = alg_add(mid, 1);
            } else {
                temp = a[mid];
                a[mid] = a[high];
                a[high] = temp;
                high = alg_sub(high, 1);
            }
        }
    }
    return 0;
}

int main(void) {
    std::vector<int> a = {2, 0, 1, 2, 0};
    int result = dutch_flag(a);
    printf("%d\n", result);
    for (int z = 0; z < 5; z++) printf("%d ", a[z]);
    printf("\n");
    // Expected a: [0, 0, 1, 2, 2]
    return 0;
}

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Dutch National Flag Partition in C
//
// PURPOSE
// Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
// grouping values around a pivot.
//
// METHOD
// Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
// advance past a one, or swap a two right and re-examine the incoming unknown value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space. Not stable.
//
// CONTRACT
// Every value must be 0, 1, or 2. Mutates the array into sorted order and 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
// 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: 0.
// Expected a after call: [0, 0, 1, 2, 2].
// 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 dutch_flag(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) && (alg_value <= 2)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    int low = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int mid = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int high = alg_sub(n, 1, &alg_error);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int temp = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (mid <= high);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        int alg_condition_1 = (a[mid] == 0);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_1) {
            temp = a[low];
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            a[low] = a[mid];
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            a[mid] = temp;
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            low = alg_add(low, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            mid = alg_add(mid, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        } else {
            int alg_condition_2 = (a[mid] == 1);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (alg_condition_2) {
                mid = alg_add(mid, 1, &alg_error);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            } else {
                temp = a[mid];
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                a[mid] = a[high];
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                a[high] = temp;
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                high = alg_sub(high, 1, &alg_error);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            }
        }
    }
    alg_result = 0;
    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[] = {2, 0, 1, 2, 0};
    int result = dutch_flag(a, 5);
    printf("%d\n", result);
    for (int z = 0; z < 5; z++) printf("%d ", a[z]);
    printf("\n");
    // Expected a: [0, 0, 1, 2, 2]
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}