chore(CPlusPlus): add binary insertion sort (#308)

* Add binary insertion sort

* Change array to vector

* Fix typo

algorithms/CPlusPlus/README.md

@@ -48,6 +48,7 @@
 9. [heap Sort](Sorting/heap-sort.cpp)
 10. [Radix Sort](Sorting/radix-sort.cpp)
 11. [Shell Sort](Sorting/shell-sort.cpp)
+12. [Binary Insertion Sort](Sorting/binary-insertion-sort.cpp)
  
 ## Strings
 1. [Rabin-Karp pattern search algo](Strings/rabin-karp.cpp)

algorithms/CPlusPlus/Sorting/binary-insertion-sort.cpp

@@ -0,0 +1,77 @@
+#include <iostream>
+#include <vector>
+
+/**
+ * In normal insertion sort there will be "i" comparisons
+ * for every i'th iteration. 
+ * 	Minimum comparison : 1
+ * 	Maximum comparison : O(i) for every i'th iteration
+ *
+ * In binary insertion sort there will be only log(i) comparisons
+ * for every i'th iteration
+ * 	Minimum comparison: 1
+ * 	Maximum comparison: O(log(i)) for every i'th iteration
+ *  
+ * Still the total time complexity of the algorithm remains the same
+ * because of the swap in each iteration
+ *
+ * Time Complexity of binary insertion sort: O(n^2)
+ */
+
+int binary_search(std::vector<int>& arr, int item, int left, int right){
+	/**
+	 * Binary Search Algorithm
+	 *
+	 * @params: `arr` array with the elements
+	 * @params: `size` size of the array
+	 *
+	 * Time complexity: O(log(n))
+	 */
+	int mid = 0;
+	while(left <= right){
+		mid = left + (right - left) / 2;
+		if(arr[mid] == item) { return mid + 1; }
+		if(arr[mid] < item ) { left = mid + 1; }
+		else		     { right = mid - 1; } 		
+	}
+	if(item > arr[left]) {  return left + 1; }
+	else { return left; }
+}
+
+void insertion_sort(std::vector<int>& arr, int size){
+	/*
+	 * Insertion Sort Algorithm
+	 *
+	 * @params: `arr` array with the elements
+	 * @params: `size` size of the array
+	 *
+	 * Time complexity: O(n^2)
+	 */
+
+	for(int i=1; i<size; i++){
+		int index = i;
+		int item = arr[i];
+		int loc = binary_search(arr, item, 0, i-1);
+		while(index-1 >= loc){
+			arr[index] = arr[index-1];
+			index--;
+		}
+		arr[index] = item;
+	}
+}
+
+int main(){
+	// I/O operation
+	//-----------------------------------------------
+	int N;
+	std::cout << "Enter total number of elements: ";
+	std::cin >> N;
+	std::vector<int> arr(N);
+	
+	std::cout << "Enter the elements: " << std::endl;
+	for(auto& i: arr){ std::cin >> i; }
+	//-------------------------------------------------
+	
+	insertion_sort(arr, N);
+	for(const auto& i: arr){ std::cout << i << " "; }
+}