feat: Reworked interpolation_search.cpp (#1855)

* feat: Reworked interpolation_search.cpp

* Update interpolation_search.cpp

* clang-format and clang-tidy fixes for c98405b3

* Update search/interpolation_search.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update search/interpolation_search.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update search/interpolation_search.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update search/interpolation_search.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for d4eac660

* Update search/interpolation_search.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update search/interpolation_search.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* fix: apply suggestions from code review

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: David Leal <halfpacho@gmail.com>

search/interpolation_search.cpp

@@ -1,61 +1,123 @@
-/**
- * \file
- * \brief [Interpolation
- * search](https://en.wikipedia.org/wiki/Interpolation_search) algorithm
- */
-#include <iostream>
 
-/** function to search the value in an array using interpolation search
+/******************************************************************************
- * \param [in] arr array to search in
+ * @file
- * \param [in] value value to search for
+ * @brief [Interpolation search
- * \param [in] len length of array
+ * algorithm](https://en.wikipedia.org/wiki/interpolation_search)
- * \returns index where the value is found
+ *
- * \returns 0 if not found
+ * @details
- */
+ * interpolation search resembles the method by which people search a telephone
-int interpolation_search(int arr[], int value, int len) {
+ * directory for a name (the key value by which the book's entries are ordered):
-    int low = 0, high, mid;
+ * in each step the algorithm calculates where in the remaining search space
-    high = len - 1;
+ * the sought item might be, based on the key values at the bounds of the search
+ * space and the value of the sought key, usually via a linear interpolation.
+ * The key value actually found at this estimated position is then compared to
+ * the key value being sought. If it is not equal, then depending on the
+ * comparison, the remaining search space is reduced to the part before or
+ * after the estimated position. This method will only work if calculations
+ * on the size of differences between key values are sensible.
 
-    while (arr[low] <= value && arr[high] >= value) {
+ * ### Complexities
-        mid = (low +
+ *
-               ((value - arr[low]) * (high - low)) / (arr[high] - arr[low]));
+ * //n is the number of element in the array.
-        if (arr[mid] > value)
+ *
-            high = mid - 1;
+ * Worst-case time complexity	O(n)                (when items are distributed
-        else if (arr[mid] < value)
+ exponentially)
-            low = mid + 1;
+ * Average time complexity	    O(log2(log2 n))
-        else
+ * space complexity  0(1)
-            return mid;
+ *
+ * @author [Lajat Manekar](https://github.com/Lazeeez)
+ * @author Unknown author
+ *******************************************************************************/
+
+#include <algorithm>  /// for std::sort function
+#include <cassert>    /// for std::assert
+#include <iostream>   /// for IO operations
+#include <vector>     /// for std::vector
+
+/******************************************************************************
+ * @namespace search
+ * @brief Searching algorithms
+ *******************************************************************************/
+namespace search {
+
+/******************************************************************************
+ * @namespace interpolation_search
+ * @brief Functions for the [Interpolation
+ *Search](https://en.wikipedia.org/wiki/interpolation_search) algorithm
+ *implementation
+ *******************************************************************************/
+namespace interpolation_search {
+
+/******************************************************************************
+ * @brief The main function which implements interpolation search
+ * @param arr vector to be searched in
+ * @param number value to be searched
+ * @returns integer index of `number` in vector `arr`
+ *******************************************************************************/
+uint64_t interpolationSearch(const std::vector<uint64_t> &arr,
+                             uint64_t number) {
+    uint64_t size = arr.size();
+    uint64_t low = 0, high = (size - 1);
+
+    // Since vector is sorted, an element present in array must be in range
+    // defined by corner
+    while (low <= high && number >= arr[low] && number <= arr[high]) {
+        if (low == high) {
+            if (arr[low] == number) {
+                return low;
+            }
+            return -1;
+        }
+        // Probing the position with keeping uniform distribution in mind.
+        uint64_t pos =
+            low +
+            ((static_cast<uint64_t>(high - low) / (arr[high] - arr[low])) *
+             (number - arr[low]));
+
+        if (arr[pos] == number) {
+            return pos;  // Condition of target found
         }
 
-    if (arr[low] == value)
+        if (arr[pos] < number) {
-        return low;
+            low = pos + 1;  // If x is larger, x is in upper part
+        }
 
+        else {
+            high = pos - 1;  // If x is smaller, x is in the lower part
+        }
+    }
     return -1;
 }
 
-/** main function */
+}  // namespace interpolation_search
+
+}  // namespace search
+
+/*******************************************************************************
+ * @brief Self-test implementation
+ * @returns void
+ *******************************************************************************/
+static void tests() {
+    // testcase
+    // array = [10, 12, 13, 16, 18, 19, 20, 21, 1, 2, 3, 4, 22, 23, 24, 33, 35,
+    // 42, 47] , Value = 33 should return 15
+    std::vector<uint64_t> arr = {{10, 12, 13, 16, 18, 19, 20, 21, 1, 2, 3, 4,
+                                  22, 23, 24, 33, 35, 42, 47}};
+    sort(arr.begin(), arr.end());
+    uint64_t number = 33;  // Element to be searched
+    uint64_t expected_answer = 15;
+    uint64_t derived_answer =
+        search::interpolation_search::interpolationSearch(arr, number);
+    std::cout << "Testcase: ";
+    assert(derived_answer == expected_answer);
+    std::cout << "Passed!\n";
+}
+
+/*******************************************************************************
+ * @brief Main function
+ * @returns 0 on exit
+ *******************************************************************************/
 int main() {
-    int n, value, re;
+    tests();  // run self-test implementations
-
-    std::cout << "Enter the size of array(less than 100) : ";
-    std::cin >> n;
-
-    int *array = new int[n];
-
-    std::cout << "array in ascending (increasing) order : " << std::endl;
-
-    for (int i = 0; i < n; i++) std::cin >> array[i];
-
-    std::cout << "Enter the value you want to search : ";
-    std::cin >> value;
-
-    re = interpolation_search(array, value, n);
-
-    if (re == -1)
-        std::cout << "Entered value is not in the array" << std::endl;
-    else
-        std::cout << "The value is at the position " << re << std::endl;
-
-    delete[] array;
     return 0;
 }