Merge operations using STL in C++ | merge(), includes(), set_union(), set_intersection(), set_difference(), ., inplace_merge,

Some of the merge operation classes are provided in C++ STL under the header file “algorithm”, which facilitates several merge operations in a easy manner. 
Some of them are mentioned below. 

1. merge(beg1, end1, beg2, end2, beg3) :- This function merges two sorted containers and stores in new container in sorted order (merge sort). It takes 5 arguments, first and last iterator of 1st container, first and last iterator of 2nd container and 1st iterator of resultant container. 
2. includes(beg1, end1, beg2, end2) :- This function is used to check whether one sorted container elements are including other sorted container elements or not. Returns true if 1st container includes 2nd container else returns false.
   

CPP

// C++ code to demonstrate the working of
// merge() and include()
#include<iostream>
#include<algorithm> // merge operations
#include<vector> // for vector
using namespace std;
int main()
{
 // Initializing 1st vector
 vector<int> v1 = {1, 3, 4, 5, 20, 30};

 // Initializing 2nd vector
 vector<int> v2 = {1, 5, 6, 7, 25, 30};

 // Declaring resultant vector
 // for merging
 vector<int> v3(12);

 // Using merge() to merge vectors v1 and v2
 // and storing result in v3
 merge(v1.begin(), v1.end(), v2.begin(),
                   v2.end(), v3.begin());

 // Displaying resultant container
 cout << "The new container after merging is :\n";
 for (int &x : v3)
     cout << x << " ";
 cout << endl;

 // Initializing new vector
 vector<int> v4 = {1, 3, 4, 5, 6, 20, 25, 30};

 // Using include() to check if v4 contains v1
 includes(v4.begin(), v4.end(), v1.begin(), v1.end())?
        cout << "v4 includes v1":
        cout << "v4 does'nt include v1";

 return 0;
}

Output 

The new container after merging is :
1 1 3 4 5 5 6 7 20 25 30 30 
v4 includes v1

Time complexity: 
The time complexity of the merge() and include() functions is O(n1 + n2) where n1 and n2 are the sizes of the two containers being merged or checked, respectively.

Space complexity:
The space complexity of the merge() and include() functions is O(n1 + n2) where n1 and n2 are the sizes of the two containers being merged or checked, respectively. This is due to the fact that both functions require an additional container of a size equal to the sum of the sizes of the two containers being merged or checked.

inplace_merge(beg1, beg2, end) :- This function is used to sort two consecutively placed sorted ranges in a single container. It takes 3 arguments, iterator to beginning of 1st sorted range, iterator to beginning of 2nd sorted range, and iterator to last position.

CPP

// C++ code to demonstrate the working of
// inplace_merge()
#include<iostream>
#include<algorithm> // merge operations
#include<vector> // for vector
using namespace std;
int main()
{

 // Initializing 1st vector
 vector<int> v1 = {1, 3, 4, 5, 20, 30};

 // Initializing 2nd vector
 vector<int> v2 = {1, 5, 6, 7, 25, 30};

 // Declaring resultant vector
 // for inplace_merge()
 vector<int> v3(12);

 // using copy to copy both vectors into
 // one container
 auto it = copy(v1.begin(), v1.end(), v3.begin());
 copy(v2.begin(), v2.end(), it);

 // Using inplace_merge() to sort the container
 inplace_merge(v3.begin(),it,v3.end());

 // Displaying resultant container
 cout << "The new container after inplace_merging is :\n";
 for (int &x : v3)
     cout << x << " ";
 cout << endl;

 return 0;

}

Output: 

The new container after inplace_merging is :
1 1 3 4 5 5 6 7 20 25 30 30 

set_union(beg1, end1, beg2, end2, beg3) :- This function computes the set union of two containers and stores in new container .It returns the iterator to the last element of resultant container. It takes 5 arguments, first and last iterator of 1st container, first and last iterator of 2nd container and 1st iterator of resultant container . The containers should be sorted and it is necessary that new container is resized to suitable size.

set_intersection(beg1, end1, beg2, end2, beg3) :- This function computes the set intersection of two containers and stores in new container .It returns the iterator to the last element of resultant container. It takes 5 arguments, first and last iterator of 1st container, first and last iterator of 2nd container and 1st iterator of resultant container . The containers should be sorted and it is necessary that new container is resized to suitable size. 
One way to implement set-union and set-intersection in sorted ranges can be found here

CPP

// C++ code to demonstrate the working of
// set_union() and set_intersection()
#include<iostream>
#include<algorithm> // for merge operations
#include<vector> // for vector
using namespace std;
int main()
{
 // Initializing 1st vector
 vector<int> v1 = {1, 3, 4, 5, 20, 30};

 // Initializing 2nd vector
 vector<int> v2 = {1, 5, 6, 7, 25, 30};

 // Declaring resultant vector
 // for union
 vector<int> v3(10);

 // Declaring resultant vector
 // for intersection
 vector<int> v4(10);

 // using set_union() to compute union  of 2
 // containers v1 and v2 and store result in v3
 auto it = set_union(v1.begin(), v1.end(), v2.begin(),
                              v2.end(), v3.begin());

 // using set_intersection() to compute intersection
 // of 2 containers v1 and v2 and store result in v4
 auto it1 = set_intersection(v1.begin(),v1.end(),
               v2.begin(), v2.end(), v4.begin());

 // resizing new container
 v3.resize(it - v3.begin());

 // resizing new container
 v4.resize(it1 - v4.begin());

 // Displaying set union
 cout << "Union of two containers is : ";
 for (int &x : v3)
     cout << x << " ";
 cout << endl;

 // Displaying set intersection
 cout << "Intersection of two containers is : ";
 for (int &x : v4)
     cout << x << " ";
 cout << endl;

 return 0;
}

Output:  

Union of two containers is : 1 3 4 5 6 7 20 25 30 
Intersection of two containers is : 1 5 30 

set_difference(beg1, end1, beg2, end2, beg3) :- This function computes the set difference of two containers and stores in new container .It returns the iterator to the last element of resultant container. It takes 5 arguments, first and last iterator of 1st container, first and last iterator of 2nd container and 1st iterator of resultant container . The containers should be sorted and it is necessary that new container is resized to suitable size.

set_symmetric_difference(beg1, end1, beg2, end2, beg3) :- This function computes the set symmetric difference of two containers and stores in new container .It returns the iterator to the last element of resultant container. It takes 5 arguments, first and last iterator of 1st container, first and last iterator of 2nd container and 1st iterator of resultant container . The containers should be sorted and it is necessary that new container is resized to suitable size.

CPP

// C++ code to demonstrate the working of
// set_difference() and set_symmetric_difference()
#include<iostream>
#include<algorithm> // for merge operations
#include<vector> // for vector
using namespace std;
int main()
{
 // Initializing 1st vector
 vector<int> v1 = {1, 3, 4, 5, 20, 30};

 // Initializing 2nd vector
 vector<int> v2 = {1, 5, 6, 7, 25, 30};

 // Declaring resultant vector
 // for difference
 vector<int> v3(10);

 // Declaring resultant vector
 // for symmetric_difference
 vector<int> v4(10);


 // using set_difference() to compute difference
 // of 2 containers v1 and v2.
 auto it = set_difference(v1.begin(), v1.end(),
              v2.begin(), v2.end(), v3.begin());

 // using set_symmetric_difference() to compute
 // symmetric_difference/ of 2 containers
 auto it1 = set_symmetric_difference(v1.begin(),
       v1.end(), v2.begin(), v2.end(), v4.begin());

 // resizing new container
 v3.resize(it - v3.begin());

 // resizing new container
 v4.resize(it1 - v4.begin());

 // Displaying set difference
 cout << "Difference of two containers is : ";
 for (int &x : v3)
     cout << x << " ";
 cout << endl;

 // Displaying set symmetric_difference
 cout << "symmetric_difference of two containers is : ";
 for (int &x : v4)
     cout << x << " ";
 cout << endl;

 return 0;
}

Output: 

Difference of two containers is : 3 4 20 
Symmetric difference of two containers is : 3 4 6 7 20 25 

The time complexity of set_difference() and set_symmetric_difference() is O(m+n) where m and n are the size of the two input containers.

The space complexity of both the functions is O(m+n) as the resulting vector would take the same size as the combined size of the two input vectors.

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