Merge pull request #671 from Divide-et-impera-11/swing

Struzik(exponential) search invented by Jon Bentley & Andrew Chi-Chih Yao

search/exponential_search.cpp

+// Copyright 2020 Divide-et-impera-11
+#include <assert.h>
+#include <iostream>
+#include <string>
+using namespaces std;
+// Binary Search Algorithm(use by struzik algorithm)
+// 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)
+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 = 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)
+/* Tha 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. */
+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;
+}
+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
+return 0;
+}