exponential_search.c File Reference

Exponential Search More...

#include <assert.h>
#include <inttypes.h>

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Macros
#define	ELEMENT   -10
	for assert for int64_t, uint16_t

Functions
int64_t	binary_search (const int64_t *arr, const uint16_t l_index, const uint16_t r_index, const int64_t n)
	used to perform the binary search over the given array
int64_t	exponential_search (const int64_t *arr, const uint16_t length, const int64_t n)
	used to perform the exponential search over the given array
static void	test ()
	used to run the self-test implementations
int	main ()
	Main function.

Detailed Description

Exponential Search

Author

Alessio Farinelli

Function Documentation

binary_search()

int64_t binary_search	(	const int64_t *	arr,
		const uint16_t	l_index,
		const uint16_t	r_index,
		const int64_t	n
	)

used to perform the binary search over the given array

Function: binary_search.

algorithm that search the index of the given item

recursive function that search the given element in

the array using the <a href="https://github.com/TheAlgorithms/Algorithms-Explanation/blob/master/en/Search%20Algorithms/Binary%20Search.md" target="_blank" >Binary Search</a>

Parameters

arr	array where search the element
l_index	start index of the array (arr) to apply the algorithm
r_index	end index of the array (arr) to apply the algorithm
n	element to find in the array (arr)

Returns

the index of the element (n) in the array (arr)

-1 if the n element wasn't found

{
    // calculate the middle index of the array
    uint16_t middle_index = l_index + ( r_index - l_index ) / 2;
    // base cases
    if ( l_index > r_index ) { return -1; }
    if ( arr[middle_index] == n ) { return middle_index; }
    // recursion
    if ( arr[middle_index] > n ) { return binary_search(arr, l_index, middle_index-1, n); } // left
    return binary_search(arr, middle_index+1, r_index, n); // right
}

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exponential_search()

int64_t exponential_search	(	const int64_t *	arr,
		const uint16_t	length,
		const int64_t	n
	)

used to perform the exponential search over the given array

Function: exponential_search.

algorithm that search the index of the given item

recursive function that take an array and quickly find the range

where to apply the binary search algorithm to find the given element

Parameters

arr	array where search the element
length	the total length of the given array (arr)
n	element to find in the array (arr)

Returns

the index of the element (n) in the array (arr)

-1 if the element wasn't found

{
    if ( length == 0 ) { return -1; }
    // find the upperbound
    uint32_t upper_bound = 1;
    while ( upper_bound <= length && arr[upper_bound] < n ) { upper_bound = upper_bound * 2; }
    // calculate the range ( between lower_boud and upper_bound )
    uint16_t lower_bound = upper_bound/2;
    if ( upper_bound > length ) { upper_bound = length; }
    // apply the binary search in the range
    return binary_search(arr, lower_bound, upper_bound, n);
}

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main()

int main

(

void

)

Main function.

Returns

0 on exit

{
    test();  // run self-test implementations
    return 0;
}

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test()

static void test ( void  )

static

used to run the self-test implementations

Self-test implementations.

Returns

void

{
    // empty array
    int64_t arr_empty[] = {};
    assert(exponential_search(arr_empty, 0, 10) == -1);
    // elent not found
    int64_t arr_found[] = {1, 2, 3};
    assert(exponential_search(arr_found, 3, 10) == -1);
    // element found in an array of length 1
    int64_t arr_one[] = {1};
    assert(exponential_search(arr_found, 1, 1) == 0);
    // find the first element in an array of length 2
    int64_t arr_first_2[] = {1, 2};
    assert(exponential_search(arr_first_2, 2, 1) == 0);
    // find the last element in an array of length 2
    int64_t arr_last_2[] = {1, 2};
    assert(exponential_search(arr_last_2, 2, 2) == 1);
    // find the first element in an array of length n
    int64_t arr_first_n[] = {-1, 2, 4, 6, 8};
    assert(exponential_search(arr_first_n, 5, -1) == 0);
    // find the last element in an array of length n
    int64_t arr_last_n[] = {-1, 2, 4, 6, 8};
    assert(exponential_search(arr_last_n, 5, 8) == 4);
    // find an element in an array of length n
    int64_t arr_middle[] = {-1, 2, 4, 6, 8};
    assert(exponential_search(arr_middle, 5, 6) == 3);
}

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