exponential_search.cpp File Reference

Exponential search algorithm More...

#include <cassert>
#include <cmath>
#include <iostream>
#include <cstring>

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Functions
template<class Type >
Type *	binary_s (Type *array, size_t size, Type key)
template<class Type >
Type *	struzik_search (Type *array, size_t size, Type key)
int	main ()

Detailed Description

Exponential search algorithm

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.

Function Documentation

binary_s()

template<class Type >

Type * binary_s ( Type * array, size_t size, Type key )

inline

Binary Search Algorithm (used by struzik_search)

• 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

  nullptr if value not found

                                                          {
    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;
}

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main()

int main

(

void

)

Main function

           {
    // 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;
}

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struzik_search()

template<class Type >

Type * struzik_search	(	Type *	array,
		size_t	size,
		Type	key )

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)

                                                         {
    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;
}

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