Merge branch 'master' into add/number_of_paths

Author: realstealthninja

backtracking/graph_coloring.cpp

@@ -20,7 +20,6 @@
 
 #include <array>     /// for std::array
 #include <iostream>  /// for IO operations
-#include <vector>    /// for std::vector
 
 /**
  * @namespace backtracking

data_structures/trie_tree.cpp

@@ -12,7 +12,6 @@
 #include <iostream>
 #include <memory>
 #include <string>
-#include <vector>
 
 /** \namespace data_structures
  * \brief Data-structure algorithms

divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp

@@ -15,7 +15,6 @@
 #include <cassert>   /// for assert
 #include <cstring>   /// for string
 #include <iostream>  /// for IO operations
-#include <vector>    /// for std::vector
 
 /**
  * @namespace divide_and_conquer

graph/breadth_first_search.cpp

@@ -52,7 +52,6 @@
 #include <map>
 #include <queue>
 #include <string>
-#include <vector>
 
 /**
  * \namespace graph

sorting/quick_sort.cpp

@@ -54,7 +54,18 @@ namespace quick_sort {
  * @param low first point of the array (starting index)
  * @param high last point of the array (ending index)
  * @returns index of the smaller element
- */
+ *  
+ *  ### Time Complexity
+ *  best case, average Case: O(nlog(n))
+ *  Worst Case: O(n^2)  (Worst case occur when the partition 
+ *  is consistently unbalanced.)
+ 
+ *  ### Space Complexity
+ *  average Case: O(log(n))
+ *  Worst Case: O(n)  
+ *  It's space complexity is due to the recursive function calls and partitioning process. 
+ */ 
+
 template <typename T>
 int partition(std::vector<T> *arr, const int &low, const int &high) {
     T pivot = (*arr)[high];  // taking the last element as pivot