exponential_search.cpp

/**
 * \file
 * \brief [Exponential search
 * algorithm](https://en.wikipedia.org/wiki/Exponential_search)
 * \copyright 2020 Divide-et-impera-11
 *
 * The algorithm try to search the range where the key should be.
 * If it has been found we do a binary search there.
 * The range of the search grows by exponential every time.
 * If the key is larger than the last element of array, the start of
 * block(block_front) will be equal to the end of block(block_size) and the
 * algorithm return null ponter, every other cases the algoritm return fom the
 * loop.
 */
#include <cassert>
#include <cmath>
#include <cstdint>
#ifdef _MSC_VER
#include <string>  // use for MS Visual C++
#else
#include <cstring>  // for all other compilers
#endif

/** Binary Search Algorithm (used by ::struzik_search)\n
 * * Time Complexity O(log n) where 'n' is the number of elements
 * * Worst Time Complexity O(log n)
 * * Best Time Complexity Ω(1)
 * * Space Complexity O(1)
 * * Auxiliary Space Complexity O(1)
 * \returns pointer to value in the array
 * \returns `nullptr` if value not found
 */
template <class Type>
inline Type* binary_s(Type* array, size_t size, Type key) {
    int32_t lower_index(0), upper_index(size - 1), middle_index;

    while (lower_index <= upper_index) {
        middle_index = std::floor((lower_index + upper_index) / 2);

        if (*(array + middle_index) < key)
            lower_index = (middle_index + 1);
        else if (*(array + middle_index) > key)
            upper_index = (middle_index - 1);
        else
            return (array + middle_index);
    }

    return nullptr;
}

/** Struzik Search Algorithm(Exponential)
 * * Time Complexity O(log i) where i is the position of search key in the list
 * * Worst Time Complexity O(log i)
 * * Best Time Complexity Ω(1)
 * * Space Complexity O(1)
 * * Auxiliary Space Complexity O(1)
 */
template <class Type>
Type* struzik_search(Type* array, size_t size, Type key) {
    uint32_t block_front(0), block_size = size == 0 ? 0 : 1;
    while (block_front != block_size) {
        if (*(array + block_size - 1) < key) {
            block_front = block_size;
            (block_size * 2 - 1 < size) ? (block_size *= 2) : block_size = size;
            continue;
        }
        return binary_s<Type>(array + block_front, (block_size - block_front),
                              key);
    }
    return nullptr;
}

/** Main function */
int main() {
    // TEST CASES
    int* sorted_array = new int[7]{7, 10, 15, 23, 70, 105, 203};
    assert(struzik_search<int>(sorted_array, 7, 0) == nullptr);
    assert(struzik_search<int>(sorted_array, 7, 1000) == nullptr);
    assert(struzik_search<int>(sorted_array, 7, 50) == nullptr);
    assert(struzik_search<int>(sorted_array, 7, 7) == sorted_array);
    // TEST CASES
    delete[] sorted_array;
    return 0;
}