Algorithms: Searching

"use strict";
// Exponential Search in JavaScript
//
// PURPOSE
// Exponential search locates a search interval by doubling its size, then uses binary
// search.
//
// METHOD
// Check index zero. Double a bound until it passes the target or the input end, then binary-
// search the bounded interval.
//
// COMPLEXITY
// O(log(p+1)) comparisons for a match near index p; O(log n) worst case, O(1) space.
//
// 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
// 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 exponential_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));
    if ((n == 0)) {
        return alg_sub(0, 1);
    }
    if ((a[0] == target)) {
        return 0;
    }
    let bound = 1;
    while (((bound < n) && (a[bound] < target))) {
        if ((bound > Math.floor(n / 2))) {
            bound = n;
        } else {
            bound = alg_mul(bound, 2);
        }
    }
    let low = Math.floor(bound / 2);
    let high = Math.min(bound, alg_sub(n, 1));
    let mid = 0;
    while ((low <= high)) {
        mid = alg_add(low, Math.floor(alg_sub(high, low) / 2));
        if ((a[mid] == target)) {
            return mid;
        }
        if ((a[mid] < target)) {
            low = alg_add(mid, 1);
        } else {
            high = alg_sub(mid, 1);
        }
    }
    return alg_sub(0, 1);
}

let a = new Int32Array([1, 3, 5, 7]);
let target = 5;
let result = exponential_search(a, target);
console.log(result);

from bisect import bisect_left

# Exponential Search in Python
#
# PURPOSE
# Exponential search locates a search interval by doubling its size, then uses binary
# search.
#
# METHOD
# Check index zero. Double a bound until it passes the target or the input end, then binary-
# search the bounded interval.
#
# COMPLEXITY
# O(log(p+1)) comparisons for a match near index p; O(log n) worst case, O(1) space.
#
# 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
# 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 exponential_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)
    if n == 0:
        return -1
    if a[0] == target:
        return 0
    bound: int = 1
    while bound < n and a[bound] < target:
        if bound > n // 2:
            bound = n
        else:
            bound *= 2
    low: int = bound // 2
    high: int = min(bound, n - 1)
    mid: int = 0
    while low <= high:
        mid = low + (high - low) // 2
        if a[mid] == target:
            return mid
        if a[mid] < target:
            low = mid + 1
        else:
            high = mid - 1
    return -1

a = [1, 3, 5, 7]
target = 5
result = exponential_search(a, target)
print(result)

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Exponential Search in C
//
// PURPOSE
// Exponential search locates a search interval by doubling its size, then uses binary
// search.
//
// METHOD
// Check index zero. Double a bound until it passes the target or the input end, then binary-
// search the bounded interval.
//
// COMPLEXITY
// O(log(p+1)) comparisons for a match near index p; O(log n) worst case, O(1) space.
//
// 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
// 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: 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 exponential_search(const int *a, size_t a_length, int target) {
    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; }
    int alg_condition_1 = (n == 0);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_condition_1) {
        alg_result = alg_sub(0, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        goto alg_cleanup;
    }
    int alg_condition_2 = (a[0] == target);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_condition_2) {
        alg_result = 0;
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        goto alg_cleanup;
    }
    int bound = 1;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = ((bound < n) && (a[bound] < target));
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        int alg_condition_3 = (bound > (n / 2));
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_3) {
            bound = n;
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        } else {
            bound = alg_mul(bound, 2, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
    }
    int low = (bound / 2);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int high = alg_min(bound, alg_sub(n, 1, &alg_error));
    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; }
    while (1) {
        int alg_condition = (low <= high);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        mid = alg_add(low, (alg_sub(high, low, &alg_error) / 2), &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        int alg_condition_4 = (a[mid] == target);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_4) {
            alg_result = mid;
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            goto alg_cleanup;
        }
        int alg_condition_5 = (a[mid] < target);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_5) {
            low = alg_add(mid, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        } else {
            high = alg_sub(mid, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
    }
    alg_result = alg_sub(0, 1, &alg_error);
    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[] = {1, 3, 5, 7};
    int target = 5;
    int result = exponential_search(a, 4, target);
    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>
// Exponential Search in C++
//
// PURPOSE
// Exponential search locates a search interval by doubling its size, then uses binary
// search.
//
// METHOD
// Check index zero. Double a bound until it passes the target or the input end, then binary-
// search the bounded interval.
//
// COMPLEXITY
// O(log(p+1)) comparisons for a match near index p; O(log n) worst case, O(1) space.
//
// 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++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: 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 exponential_search(const std::vector<int>& a, int target) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    if ((n == 0)) {
        return alg_sub(0, 1);
    }
    if ((a[0] == target)) {
        return 0;
    }
    int bound = 1;
    while (((bound < n) && (a[bound] < target))) {
        if ((bound > (n / 2))) {
            bound = n;
        } else {
            bound = alg_mul(bound, 2);
        }
    }
    int low = (bound / 2);
    int high = alg_min(bound, alg_sub(n, 1));
    int mid = 0;
    while ((low <= high)) {
        mid = alg_add(low, (alg_sub(high, low) / 2));
        if ((a[mid] == target)) {
            return mid;
        }
        if ((a[mid] < target)) {
            low = alg_add(mid, 1);
        } else {
            high = alg_sub(mid, 1);
        }
    }
    return alg_sub(0, 1);
}

int main(void) {
    std::vector<int> a = {1, 3, 5, 7};
    int target = 5;
    int result = exponential_search(a, target);
    printf("%d\n", result);
    return 0;
}

using System;
// Exponential Search in C#
//
// PURPOSE
// Exponential search locates a search interval by doubling its size, then uses binary
// search.
//
// METHOD
// Check index zero. Double a bound until it passes the target or the input end, then binary-
// search the bounded interval.
//
// COMPLEXITY
// O(log(p+1)) comparisons for a match near index p; O(log n) worst case, O(1) space.
//
// 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 exponential_search(ReadOnlySpan<int> a, int target) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            if ((n == 0)) {
                return (-1);
            }
            if ((a[0] == target)) {
                return 0;
            }
            int bound = 1;
            while (((bound < n) && (a[bound] < target))) {
                if ((bound > (n / 2))) {
                    bound = n;
                } else {
                    bound = (bound * 2);
                }
            }
            int low = (bound / 2);
            int high = Math.Min(bound, (n - 1));
            int mid = 0;
            while ((low <= high)) {
                mid = (low + ((high - low) / 2));
                if ((a[mid] == target)) {
                    return mid;
                }
                if ((a[mid] < target)) {
                    low = (mid + 1);
                } else {
                    high = (mid - 1);
                }
            }
            return (-1);
        }
    }

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