feat: add binary_insertion_sort (#1850)

* Add binary_insertion_sort.cpp

* Update binary_insertion_sort.cpp

* Update sorting/binary_insertion_sort.cpp

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

* Update binary_insertion_sort.cpp

* Update binary_insertion_sort.cpp

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for d48126b7

* clang-format and clang-tidy fixes for 30cafcab

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com>

DIRECTORY.md

@@ -320,6 +320,7 @@
 
 ## Sorting
   * [Bead Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bead_sort.cpp)
+  * [Binary Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/binary_insertion_sort.cpp)
   * [Bitonic Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bitonic_sort.cpp)
   * [Bogo Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bogo_sort.cpp)
   * [Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bubble_sort.cpp)

sorting/binary_insertion_sort.cpp

@@ -0,0 +1,146 @@
+/**
+ * \file
+ * \brief [Binary Insertion Sort Algorithm
+ * (Insertion Sort)](https://en.wikipedia.org/wiki/Insertion_sort)
+ *
+ * \details
+ * If the cost of comparisons exceeds the cost of swaps, as is the case for
+ * example with string keys stored by reference or with human interaction (such
+ * as choosing one of a pair displayed side-by-side), then using binary
+ * insertion sort may yield better performance. Binary insertion sort employs a
+ * binary search to determine the correct location to insert new elements, and
+ * therefore performs ⌈log2 n⌉ comparisons in the worst case. When each element
+ * in the array is searched for and inserted this is O(n log n). The algorithm
+ * as a whole still has a running time of O(n2) on average because of the series
+ * * of swaps required for each insertion. However it has several advantages
+ * such as
+ * 1. Easy to implement
+ * 2. For small set of data it is quite efficient
+ * 3. More efficient that other Quadratic complexity algorithms like
+ *    Selection sort or bubble sort.
+ * 4. It is efficient to use it when the cost of comparison is high.
+ * 5. It's stable that is it does not change the relative order of
+ *    elements with equal keys.
+ * 6. It can sort the array or list as it receives.
+ *
+ * Example execution steps:
+ * 1. Suppose initially we have
+ * \f{bmatrix}{40 &30 &20 &50 &10\f}
+ * 2. We start traversing from 40 till we reach 10
+ * when we reach at 30 we find that it is not at it's correct place so we take
+ * 30 and place it at a correct position thus the array will become
+ * \f{bmatrix}{30 &40 &20 &50 &10\f}
+ * 3. In the next iteration we are at 20 we find that this is also misplaced so
+ * we place it at the correct sorted position thus the array in this iteration
+ * becomes
+ * \f{bmatrix}{20 &30 &40 &50 &10\f}
+ * 4. We do not do anything with 50 and move on to the next iteration and
+ * select 10 which is misplaced and place it at correct position. Thus, we have
+ * \f{bmatrix}{10 &20 &30 &40 &50\f}
+ */
+
+#include <algorithm>  /// for algorithm functions
+#include <cassert>    /// for assert
+#include <iostream>   /// for IO operations
+#include <vector>     /// for working with vectors
+
+/**
+ * \namespace sorting
+ * @brief Sorting algorithms
+ */
+namespace sorting {
+
+/**
+ * \brief Binary search function to find the most suitable pace for an element.
+ * \tparam T The generic data type.
+ * \param arr The actual vector in which we are searching a suitable place for
+ * the element. \param val The value for which suitable place is to be found.
+ * \param low The lower bound of the range we are searching in.
+ * \param high The upper bound of the range we are searching in.
+ * \returns the index of most suitable position of val.
+ */
+template <class T>
+int64_t binary_search(std::vector<T> &arr, T val, int64_t low, int64_t high) {
+    if (high <= low) {
+        return (val > arr[low]) ? (low + 1) : low;
+    }
+    int64_t mid = low + (high - low) / 2;
+    if (arr[mid] > val) {
+        return binary_search(arr, val, low, mid - 1);
+    } else if (arr[mid] < val) {
+        return binary_search(arr, val, mid + 1, high);
+    } else {
+        return mid + 1;
+    }
+}
+
+/**
+ * \brief Insertion sort function to sort the vector.
+ * \tparam T The generic data type.
+ * \param arr The actual vector to sort.
+ * \returns Void.
+ */
+template <typename T>
+void insertionSort_binsrch(std::vector<T> &arr) {
+    int64_t n = arr.size();
+
+    for (int64_t i = 1; i < n; i++) {
+        T key = arr[i];
+        int64_t j = i - 1;
+        int64_t loc = sorting::binary_search(arr, key, 0, j);
+        while (j >= loc) {
+            arr[j + 1] = arr[j];
+            j--;
+        }
+        arr[j + 1] = key;
+    }
+}
+}  // namespace sorting
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    /* descriptions of the following test */
+    /* 1st test:
+       [5, -3, -1, -2, 7] returns [-3, -2, -1, 5, 7] */
+    std::vector<int64_t> arr1({5, -3, -1, -2, 7});
+    std::cout << "1st test... ";
+    sorting::insertionSort_binsrch(arr1);
+    assert(std::is_sorted(std::begin(arr1), std::end(arr1)));
+    std::cout << "passed" << std::endl;
+
+    /* 2nd test:
+       [12, 26, 15, 91, 32, 54, 41] returns [12, 15, 26, 32, 41, 54, 91] */
+    std::vector<int64_t> arr2({12, 26, 15, 91, 32, 54, 41});
+    std::cout << "2nd test... ";
+    sorting::insertionSort_binsrch(arr2);
+    assert(std::is_sorted(std::begin(arr2), std::end(arr2)));
+    std::cout << "passed" << std::endl;
+
+    /* 3rd test:
+       [7.1, -2.5, -4.0, -2.1, 5.7] returns [-4.0, -2.5, -2.1, 5.7, 7.1] */
+    std::vector<float> arr3({7.1, -2.5, -4.0, -2.1, 5.7});
+    std::cout << "3rd test... ";
+    sorting::insertionSort_binsrch(arr3);
+    assert(std::is_sorted(std::begin(arr3), std::end(arr3)));
+    std::cout << "passed" << std::endl;
+
+    /* 4th test:
+       [12.8, -3.7, -20.7, -7.1, 2.2] returns [-20.7, -7.1, -3.7, 2.2, 12.8] */
+    std::vector<float> arr4({12.8, -3.7, -20.7, -7.1, 2.2});
+    std::cout << "4th test... ";
+    sorting::insertionSort_binsrch(arr4);
+    assert(std::is_sorted(std::begin(arr4), std::end(arr4)));
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @return 0 on exit.
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}

strings/brute_force_string_searching.cpp

@@ -45,13 +45,14 @@ const std::vector<std::vector<std::string>> test_set = {
 
 /** Main function */
 int main() {
-    for (size_t i = 0; i < test_set.size(); i++) {
-        int output = brute_force(test_set[i][0], test_set[i][1]);
+    for (const auto &i : test_set) {
+        int output = brute_force(i[0], i[1]);
 
-        if (std::to_string(output) == test_set[i][2])
+        if (std::to_string(output) == i[2]) {
             std::cout << "success\n";
-        else
+        } else {
             std::cout << "failure\n";
+        }
     }
     return 0;
 }