Algorithms: String Algorithms

using System;
// Manacher Longest Palindromic Substring in C#
//
// PURPOSE
// Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in
// linear time.
//
// METHOD
// Compute odd and even center radii in separate passes. Reuse the mirror radius within the
// current rightmost palindrome, then expand only beyond its known boundary.
//
// COMPLEXITY
// O(n) time and O(n) auxiliary space.
//
// CONTRACT
// Integer tokens. Returns longest palindrome LENGTH; empty input returns zero.
// 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: 4.
// 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 manacher(ReadOnlySpan<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int[] radius = new int[alg_size((n + 1))];
            int parity = 0;
            int left = 0;
            int right = (-1);
            int i = 0;
            int k = 0;
            int best = 0;
            while ((parity < 2)) {
                left = 0;
                right = (-1);
                i = 0;
                while ((i < n)) {
                    k = (1 - parity);
                    if ((i <= right)) {
                        k = Math.Min(radius[(((left + right) - i) + parity)], ((right - i) + 1));
                    }
                    while (((((i - k) - parity) >= 0) && ((i + k) < n) && (a[((i - k) - parity)] == a[(i + k)]))) {
                        k = (k + 1);
                    }
                    radius[i] = k;
                    best = Math.Max(best, (((2 * k) - 1) + parity));
                    if ((((i + k) - 1) > right)) {
                        left = (((i - k) - parity) + 1);
                        right = ((i + k) - 1);
                    }
                    i = (i + 1);
                }
                parity = (parity + 1);
            }
            return best;
        }
    }

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

<?php
declare(strict_types=1);
// Manacher Longest Palindromic Substring in PHP
//
// PURPOSE
// Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in
// linear time.
//
// METHOD
// Compute odd and even center radii in separate passes. Reuse the mirror radius within the
// current rightmost palindrome, then expand only beyond its known boundary.
//
// COMPLEXITY
// O(n) time and O(n) auxiliary space.
//
// CONTRACT
// Integer tokens. Returns longest palindrome LENGTH; empty input returns zero.
// 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: 4.
// 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 manacher(array $a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $radius = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $parity = 0;
    $left = 0;
    $right = alg_sub(0, 1);
    $i = 0;
    $k = 0;
    $best = 0;
    while (($parity < 2)) {
        $left = 0;
        $right = alg_sub(0, 1);
        $i = 0;
        while (($i < $n)) {
            $k = alg_sub(1, $parity);
            if (($i <= $right)) {
                $k = min($radius[alg_add(alg_sub(alg_add($left, $right), $i), $parity)], alg_add(alg_sub($right, $i), 1));
            }
            while (((alg_sub(alg_sub($i, $k), $parity) >= 0) && (alg_add($i, $k) < $n) && ($a[alg_sub(alg_sub($i, $k), $parity)] == $a[alg_add($i, $k)]))) {
                $k = alg_add($k, 1);
            }
            $radius[$i] = $k;
            $best = max($best, alg_add(alg_sub(alg_mul(2, $k), 1), $parity));
            if ((alg_sub(alg_add($i, $k), 1) > $right)) {
                $left = alg_add(alg_sub(alg_sub($i, $k), $parity), 1);
                $right = alg_sub(alg_add($i, $k), 1);
            }
            $i = alg_add($i, 1);
        }
        $parity = alg_add($parity, 1);
    }
    return $best;
}

$a = [1, 2, 2, 1];
$result = manacher($a);
echo $result, PHP_EOL;

// Rabin Karp Pattern Matching in Java
//
// PURPOSE
// Rabin-Karp uses a rolling hash to filter candidate matches, then compares tokens to
// guarantee correctness despite hash collisions.
//
// METHOD
// Hash the pattern and first window modulo a small prime. At each position verify matching
// hashes, then remove the old token and append the new one.
//
// COMPLEXITY
// Expected O(n+m) time on suitable data; O(nm) worst case due to verification. O(1)
// auxiliary space.
//
// CONTRACT
// Tokens are integers in [0,255]. Empty pattern matches at zero. Returns first index or -1;
// not a cryptographic hash.
// 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: 2.
// 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 rabin_karp(int[] text, int[] pattern) {
        java.util.Objects.requireNonNull(text, "text");
        java.util.Objects.requireNonNull(pattern, "pattern");
        int n = text.length;
        int m = pattern.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require(((m >= 0) && (m <= 1000000)));
        alg_require((pattern.length == m));
        alg_require((text.length == n));
        for (int alg_i = 0; alg_i < text.length; alg_i++) {
            int alg_value = text[alg_i];
            alg_require(((alg_value >= 0) && (alg_value <= 255)));
        }
        for (int alg_i = 0; alg_i < pattern.length; alg_i++) {
            int alg_value = pattern[alg_i];
            alg_require(((alg_value >= 0) && (alg_value <= 255)));
        }
        if ((m == 0)) {
            return 0;
        }
        if ((m > n)) {
            return Math.negateExact(1);
        }
        int power = 1;
        int target_hash = 0;
        int window_hash = 0;
        int i = 0;
        int j = 0;
        while ((i < m)) {
            target_hash = (Math.addExact(Math.multiplyExact(target_hash, 256), pattern[i]) % 10007);
            window_hash = (Math.addExact(Math.multiplyExact(window_hash, 256), text[i]) % 10007);
            if ((i < Math.subtractExact(m, 1))) {
                power = (Math.multiplyExact(power, 256) % 10007);
            }
            i = Math.addExact(i, 1);
        }
        i = 0;
        while ((i <= Math.subtractExact(n, m))) {
            if ((target_hash == window_hash)) {
                j = 0;
                while (((j < m) && (text[Math.addExact(i, j)] == pattern[j]))) {
                    j = Math.addExact(j, 1);
                }
                if ((j == m)) {
                    return i;
                }
            }
            if ((i < Math.subtractExact(n, m))) {
                window_hash = (Math.addExact(Math.subtractExact(window_hash, (Math.multiplyExact(text[i], power) % 10007)), 10007) % 10007);
                window_hash = (Math.addExact(Math.multiplyExact(window_hash, 256), text[Math.addExact(i, m)]) % 10007);
            }
            i = Math.addExact(i, 1);
        }
        return Math.negateExact(1);
    }

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

"use strict";
// Rabin Karp Pattern Matching in JavaScript
//
// PURPOSE
// Rabin-Karp uses a rolling hash to filter candidate matches, then compares tokens to
// guarantee correctness despite hash collisions.
//
// METHOD
// Hash the pattern and first window modulo a small prime. At each position verify matching
// hashes, then remove the old token and append the new one.
//
// COMPLEXITY
// Expected O(n+m) time on suitable data; O(nm) worst case due to verification. O(1)
// auxiliary space.
//
// CONTRACT
// Tokens are integers in [0,255]. Empty pattern matches at zero. Returns first index or -1;
// not a cryptographic hash.
// 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: 2.
// 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 rabin_karp(text, pattern) {
    alg_require(text instanceof Int32Array);
    alg_require(pattern instanceof Int32Array);
    let n = text.length;
    let m = pattern.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require((pattern.length == m));
    alg_require((text.length == n));
    for (let alg_i = 0; alg_i < text.length; alg_i++) {
        let alg_value = text[alg_i];
        alg_require(((alg_value >= 0) && (alg_value <= 255)));
    }
    for (let alg_i = 0; alg_i < pattern.length; alg_i++) {
        let alg_value = pattern[alg_i];
        alg_require(((alg_value >= 0) && (alg_value <= 255)));
    }
    if ((m == 0)) {
        return 0;
    }
    if ((m > n)) {
        return alg_sub(0, 1);
    }
    let power = 1;
    let target_hash = 0;
    let window_hash = 0;
    let i = 0;
    let j = 0;
    while ((i < m)) {
        target_hash = (alg_add(alg_mul(target_hash, 256), pattern[i]) % 10007);
        window_hash = (alg_add(alg_mul(window_hash, 256), text[i]) % 10007);
        if ((i < alg_sub(m, 1))) {
            power = (alg_mul(power, 256) % 10007);
        }
        i = alg_add(i, 1);
    }
    i = 0;
    while ((i <= alg_sub(n, m))) {
        if ((target_hash == window_hash)) {
            j = 0;
            while (((j < m) && (text[alg_add(i, j)] == pattern[j]))) {
                j = alg_add(j, 1);
            }
            if ((j == m)) {
                return i;
            }
        }
        if ((i < alg_sub(n, m))) {
            window_hash = (alg_add(alg_sub(window_hash, (alg_mul(text[i], power) % 10007)), 10007) % 10007);
            window_hash = (alg_add(alg_mul(window_hash, 256), text[alg_add(i, m)]) % 10007);
        }
        i = alg_add(i, 1);
    }
    return alg_sub(0, 1);
}

let text = new Int32Array([1, 2, 1, 2, 3]);
let pattern = new Int32Array([1, 2, 3]);
let result = rabin_karp(text, pattern);
console.log(result);

from bisect import bisect_left

# Rabin Karp Pattern Matching in Python
#
# PURPOSE
# Rabin-Karp uses a rolling hash to filter candidate matches, then compares tokens to
# guarantee correctness despite hash collisions.
#
# METHOD
# Hash the pattern and first window modulo a small prime. At each position verify matching
# hashes, then remove the old token and append the new one.
#
# COMPLEXITY
# Expected O(n+m) time on suitable data; O(nm) worst case due to verification. O(1)
# auxiliary space.
#
# CONTRACT
# Tokens are integers in [0,255]. Empty pattern matches at zero. Returns first index or -1;
# not a cryptographic hash.
# 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: 2.
# 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 rabin_karp(text: list[int], pattern: list[int]) -> int:
    alg_require(isinstance(text, (list, tuple)) and len(text) <= 1000000)
    alg_require(isinstance(pattern, (list, tuple)) and len(pattern) <= 1000000)
    n: int = len(text)
    m: int = len(pattern)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(m >= 0 and m <= 1000000)
    alg_require(len(pattern) == m)
    alg_require(len(text) == n)
    for value in text:
        alg_require(value >= 0 and value <= 255)
    for value in pattern:
        alg_require(value >= 0 and value <= 255)
    if m == 0:
        return 0
    if m > n:
        return -1
    power: int = 1
    target_hash: int = 0
    window_hash: int = 0
    i: int = 0
    j: int = 0
    while i < m:
        target_hash = (target_hash * 256 + pattern[i]) % 10007
        window_hash = (window_hash * 256 + text[i]) % 10007
        if i < m - 1:
            power = power * 256 % 10007
        i += 1
    i = 0
    while i <= n - m:
        if target_hash == window_hash:
            j = 0
            while j < m and text[i + j] == pattern[j]:
                j += 1
            if j == m:
                return i
        if i < n - m:
            window_hash = (window_hash - text[i] * power % 10007 + 10007) % 10007
            window_hash = (window_hash * 256 + text[i + m]) % 10007
        i += 1
    return -1

text = [1, 2, 1, 2, 3]
pattern = [1, 2, 3]
result = rabin_karp(text, pattern)
print(result)