Algorithms: Searching

using System;
// Ternary Search in Sorted Arrays in C#
//
// PURPOSE
// Ternary search compares two interior positions to discard two thirds of a sorted interval.
//
// METHOD
// Compute two partition positions. Return a matching position, otherwise retain the left,
// middle, or right third containing the target.
//
// COMPLEXITY
// O(log n) time, O(1) space. Binary search generally uses fewer comparisons; this is
// distinct from optimization on unimodal functions.
//
// CONTRACT
// Ascending input; returns any matching index or -1.
// 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: 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 ternary_search(ReadOnlySpan<int> a, int target) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int low = 0;
            int high = (n - 1);
            int third = 0;
            int first = 0;
            int second = 0;
            while ((low <= high)) {
                third = ((high - low) / 3);
                first = (low + third);
                second = (high - third);
                if ((a[first] == target)) {
                    return first;
                }
                if ((a[second] == target)) {
                    return second;
                }
                if ((target < a[first])) {
                    high = (first - 1);
                } else {
                    if ((target > a[second])) {
                        low = (second + 1);
                    } else {
                        low = (first + 1);
                        high = (second - 1);
                    }
                }
            }
            return (-1);
        }
    }

    static void Main() {
        int[] a = new int[] {1, 3, 5, 7};
        int target = 5;
        int result = ternary_search(a, target);
        Console.WriteLine(result);
    }
}

<?php
declare(strict_types=1);
// Ternary Search in Sorted Arrays in PHP
//
// PURPOSE
// Ternary search compares two interior positions to discard two thirds of a sorted interval.
//
// METHOD
// Compute two partition positions. Return a matching position, otherwise retain the left,
// middle, or right third containing the target.
//
// COMPLEXITY
// O(log n) time, O(1) space. Binary search generally uses fewer comparisons; this is
// distinct from optimization on unimodal functions.
//
// CONTRACT
// Ascending input; returns any matching index or -1.
// 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: 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 ternary_search(array $a, int $target): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $low = 0;
    $high = alg_sub($n, 1);
    $third = 0;
    $first = 0;
    $second = 0;
    while (($low <= $high)) {
        $third = intdiv(alg_sub($high, $low), 3);
        $first = alg_add($low, $third);
        $second = alg_sub($high, $third);
        if (($a[$first] == $target)) {
            return $first;
        }
        if (($a[$second] == $target)) {
            return $second;
        }
        if (($target < $a[$first])) {
            $high = alg_sub($first, 1);
        } else {
            if (($target > $a[$second])) {
                $low = alg_add($second, 1);
            } else {
                $low = alg_add($first, 1);
                $high = alg_sub($second, 1);
            }
        }
    }
    return alg_sub(0, 1);
}

$a = [1, 3, 5, 7];
$target = 5;
$result = ternary_search($a, $target);
echo $result, PHP_EOL;

// Interpolation Search in Java
//
// PURPOSE
// Interpolation search estimates the target position from endpoint values, which can help on
// roughly uniform numeric data.
//
// METHOD
// Estimate a position proportional to the target value between endpoint values. Compare
// there and discard the impossible side. Handle equal endpoints separately.
//
// COMPLEXITY
// Expected O(log log n) comparisons for suitable uniform distributions; O(n) worst case,
// O(1) space.
//
// CONTRACT
// Ascending nonnegative integers <= 10000; n <= 10000 so the interpolation product fits
// signed 32-bit. Returns any matching index or -1.
// 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 interpolation_search(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));
        alg_require((n <= 10000));
        for (int alg_i = 0; alg_i < a.length; alg_i++) {
            int alg_value = a[alg_i];
            alg_require(((alg_value >= 0) && (alg_value <= 10000)));
        }
        int low = 0;
        int high = Math.subtractExact(n, 1);
        int pos = 0;
        while (((low <= high) && (target >= a[low]) && (target <= a[high]))) {
            if ((a[low] == a[high])) {
                return low;
            }
            pos = Math.addExact(low, (Math.multiplyExact(Math.subtractExact(target, a[low]), Math.subtractExact(high, low)) / Math.subtractExact(a[high], a[low])));
            if ((a[pos] == target)) {
                return pos;
            }
            if ((a[pos] < target)) {
                low = Math.addExact(pos, 1);
            } else {
                high = Math.subtractExact(pos, 1);
            }
        }
        return Math.negateExact(1);
    }

    public static void main(String[] args) {
        int[] a = new int[] {0, 10, 20, 30};
        int target = 20;
        int result = interpolation_search(a, target);
        System.out.println(result);
    }
}

"use strict";
// Interpolation Search in JavaScript
//
// PURPOSE
// Interpolation search estimates the target position from endpoint values, which can help on
// roughly uniform numeric data.
//
// METHOD
// Estimate a position proportional to the target value between endpoint values. Compare
// there and discard the impossible side. Handle equal endpoints separately.
//
// COMPLEXITY
// Expected O(log log n) comparisons for suitable uniform distributions; O(n) worst case,
// O(1) space.
//
// CONTRACT
// Ascending nonnegative integers <= 10000; n <= 10000 so the interpolation product fits
// signed 32-bit. Returns any matching index or -1.
// 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 interpolation_search(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));
    alg_require((n <= 10000));
    for (let alg_i = 0; alg_i < a.length; alg_i++) {
        let alg_value = a[alg_i];
        alg_require(((alg_value >= 0) && (alg_value <= 10000)));
    }
    let low = 0;
    let high = alg_sub(n, 1);
    let pos = 0;
    while (((low <= high) && (target >= a[low]) && (target <= a[high]))) {
        if ((a[low] == a[high])) {
            return low;
        }
        pos = alg_add(low, Math.floor(alg_mul(alg_sub(target, a[low]), alg_sub(high, low)) / alg_sub(a[high], a[low])));
        if ((a[pos] == target)) {
            return pos;
        }
        if ((a[pos] < target)) {
            low = alg_add(pos, 1);
        } else {
            high = alg_sub(pos, 1);
        }
    }
    return alg_sub(0, 1);
}

let a = new Int32Array([0, 10, 20, 30]);
let target = 20;
let result = interpolation_search(a, target);
console.log(result);

from bisect import bisect_left

# Interpolation Search in Python
#
# PURPOSE
# Interpolation search estimates the target position from endpoint values, which can help on
# roughly uniform numeric data.
#
# METHOD
# Estimate a position proportional to the target value between endpoint values. Compare
# there and discard the impossible side. Handle equal endpoints separately.
#
# COMPLEXITY
# Expected O(log log n) comparisons for suitable uniform distributions; O(n) worst case,
# O(1) space.
#
# CONTRACT
# Ascending nonnegative integers <= 10000; n <= 10000 so the interpolation product fits
# signed 32-bit. Returns any matching index or -1.
# 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 interpolation_search(a: list[int], target: int) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    alg_require(type(target) is int and -2147483648 <= target <= 2147483647)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    alg_require(n <= 10000)
    for value in a:
        alg_require(value >= 0 and value <= 10000)
    low: int = 0
    high: int = n - 1
    pos: int = 0
    while low <= high and target >= a[low] and (target <= a[high]):
        if a[low] == a[high]:
            return low
        pos = low + (target - a[low]) * (high - low) // (a[high] - a[low])
        if a[pos] == target:
            return pos
        if a[pos] < target:
            low = pos + 1
        else:
            high = pos - 1
    return -1

a = [0, 10, 20, 30]
target = 20
result = interpolation_search(a, target)
print(result)