Add binary_insertion_sort.cpp

sorting/binary_insertion_sort.cpp

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+/**
+ * \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>
+#include <cassert>
+#include <iostream>
+#include <vector>
+
+/**
+ * \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>
+int binary_search(std::vector<T> &arr,T val,int low,int high)
+{
+    if (high <= low)
+        return (val > arr[low]) ? (low + 1) : low;
+    
+    int 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) {
+    int n = arr.size();
+
+    for (int i = 1; i < n; i++) {
+        T key = arr[i];
+        int j = i - 1;
+        int 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
+ */
+void test() {
+    /* descriptions of the following test */
+    /* 1st test: 
+       [5, -3, -1, -2, 7] returns [-3, -2, -1, 5, 7] */
+    std::vector<int> arr1({5, -3, -1, -2, 7});
+    std::cout << "Test 1... ";
+    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<int> arr2({12, 26, 15, 91, 32, 54, 41});
+    std::cout << "Test 2... ";
+    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 << "Test 3... ";
+    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 << "Test 4... ";
+    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;
+}