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document exponential search

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Krishna Vedala 2020-05-28 19:54:37 -04:00
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search/exponential_search.cpp
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@ -1,20 +1,42 @@
// Copyright 2020 Divide-et-impera-11 /**
* \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 <cassert>
#include <cmath> #include <cmath>
#include <iostream> #include <iostream>
#include <string> #ifdef _MSC_VER
#include <string> // use for MS Visual C++
#else
#include <cstring> // for all other compilers
#endif
// Binary Search Algorithm(use by struzik algorithm) /** Binary Search Algorithm (used by ::struzik_search)\n
// Time Complexity O(log n) where 'n' is the number of elements * * Time Complexity O(log n) where 'n' is the number of elements
// Worst Time Complexity O(log n) * * Worst Time Complexity O(log n)
// Best Time Complexity Ω(1) * * Best Time Complexity Ω(1)
// Space Complexity O(1) * * Space Complexity O(1)
// Auxiliary 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> template <class Type>
inline Type* binary_s(Type* array, size_t size, Type key) { inline Type* binary_s(Type* array, size_t size, Type key) {
int32_t lower_index(0), upper_index(size - 1), middle_index; int32_t lower_index(0), upper_index(size - 1), middle_index;
while (lower_index <= upper_index) { while (lower_index <= upper_index) {
middle_index = std::floor((lower_index + upper_index) / 2); middle_index = std::floor((lower_index + upper_index) / 2);
if (*(array + middle_index) < key) if (*(array + middle_index) < key)
lower_index = (middle_index + 1); lower_index = (middle_index + 1);
else if (*(array + middle_index) > key) else if (*(array + middle_index) > key)
@ -22,21 +44,17 @@ inline Type* binary_s(Type* array, size_t size, Type key) {
else else
return (array + middle_index); return (array + middle_index);
} }
return nullptr; return nullptr;
} }
// Struzik Search Algorithm(Exponential)
// Time Complexity O(log i)where i is the position of search key in the list /** Struzik Search Algorithm(Exponential)
// Worst Time Complexity O(log i) * * Time Complexity O(log i) where i is the position of search key in the list
// Best Time Complexity Ω(1) * * Worst Time Complexity O(log i)
// Space Complexity O(1) * * Best Time Complexity Ω(1)
// Auxiliary Space Complexity O(1) * * Space Complexity O(1)
/* Tha algorithm try to search the range where the key should be. * * Auxiliary Space Complexity O(1)
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. */
template <class Type> template <class Type>
Type* struzik_search(Type* array, size_t size, Type key) { Type* struzik_search(Type* array, size_t size, Type key) {
uint32_t block_front(0), block_size = size == 0 ? 0 : 1; uint32_t block_front(0), block_size = size == 0 ? 0 : 1;
@ -51,6 +69,8 @@ Type* struzik_search(Type* array, size_t size, Type key) {
} }
return nullptr; return nullptr;
} }
/** Main function */
int main() { int main() {
// TEST CASES // TEST CASES
int* sorted_array = new int[7]{7, 10, 15, 23, 70, 105, 203}; int* sorted_array = new int[7]{7, 10, 15, 23, 70, 105, 203};