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# set_union

Processes the sorted union of two ranges
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### Key Facts

Gyroscopic Couple: The rate of change of angular momentum () = (In the limit).
• = Moment of Inertia.
• = Angular velocity
• = Angular velocity of precession.

Blaise Pascal (1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.

Leonhard Euler (1707-1783) was a pioneering Swiss mathematician and physicist.

## Definition

The set_union() algorithm is defined in the standard header <algorithm> and in the nonstandard backward-compatibility header <algo.h>.

## Interface

#include <algorithm>
template < class InputIterator1, class InputIterator2, class OutputIterator >
OutputIterator set_union(
InputIterator1 first1,
InputIterator1 last1,
InputIterator2 first2,
InputIterator2 last2,
OutputIterator result
);
template < class InputIterator1, class InputIterator2, class OutputIterator, class BinaryPredicate >
OutputIterator set_union(
InputIterator1 first1,
InputIterator1 last1,
InputIterator2 first2,
InputIterator2 last2,
OutputIterator result,
BinaryPredicate comp
);

Parameters:
Parameter Description
first1 An input iterator addressing the position of the first element in the first of two sorted source ranges to be united and sorted into a single range representing the union of the two source ranges
last1 An input iterator addressing the position one past the last element in the first of two sorted source ranges to be united and sorted into a single range representing the union of the two source ranges
first2 An input iterator addressing the position of the first element in second of two consecutive sorted source ranges to be united and sorted into a single range representing the union of the two source ranges
last2 An input iterator addressing the position one past the last element in second of two consecutive sorted source ranges to be united and sorted into a single range representing the union of the two source ranges
result An output iterator addressing the position of the first element in the destination range where the two source ranges are to be united into a single sorted range representing the union of the two source ranges
comp User-defined predicate function object that defines the sense in which one element is greater than another. The binary predicate takes two arguments and should return true when the first element is less than the second element and false otherwise

## Description

Set_union function creates a sorted range beginning at result consisting of all elements present in one or both sorted ranges [first1, last1) and [first2, last2).
If an element is found m times in [first1, last1) and n times in [first2, last2) (where m or n may be zero), then it will appear max(m, n) times in the output range.

The first version compares objects using operator<, and the second compares objects using a function object comp.

## Return Value

Returns an iterator on the element following the last of the build sequence.

## Complexity

The complexity is linear; performs at most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

### References

Example:
##### Example - set_union algorithm
Problem
This program illustrates the use of the STL set_union() algorithm (default version) to find the values that are in a first vector of integers or in a second vector of integers (or in both), and write them out to a third vector of integers.
Workings
#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int main()
{
int a1[] = {11, 12, 12, 12, 12, 13, 14, 15};
vector<int> v1(a1, a1+8);

cout <<"\nHere are the values in the vector v1:\n";
for (vector<int>::size_type i=0; i<v1.size(); i++)
cout <<v1.at(i)<<" ";

int a2[] = {11, 12, 12, 13, 13, 16, 17, 18};
vector<int> v2(a2, a2+8);

cout <<"\nHere are the values in the vector v2:\n";
for (vector<int>::size_type i=0; i<v2.size(); i++)
cout <<v2.at(i)<<" ";

int a3[] = {101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115};
vector<int> v3(a3, a3+15);

cout <<"\nHere are the values in the vector v3:\n";
for (vector<int>::size_type i=0; i<v3.size(); i++)
cout <<v3.at(i)<<" ";

cout <<"\nNow we find the values that are in v1 or in v2, "
"or in both,\nand write them out to v3, starting at the "
"beginning of v3.";

vector<int>::iterator p;
p = set_union(v1.begin(), v1.end(), v2.begin(), v2.end(), v3.begin());

cout <<"\nHere are the revised contents of v3:\n";
for (vector<int>::size_type i=0; i<v3.size(); i++)
cout <<v3.at(i)<<" ";

cout <<"\nThe iterator returned by the algorithm is pointing at the value "<<*p<<".";

return 0;
}
Solution
Output:

Here are the values in the vector v1:
11 12 12 12 12 13 14 15

Here are the values in the vector v2:
11 12 12 13 13 16 17 18

Here are the values in the vector v3:
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115

Now we find the values that are in v1 or in v2, or in both,
and write them out to v3, starting at the beginning of v3.

Here are the revised contents of v3:
11 12 12 12 12 13 13 14 15 16 17 18 113 114 115

The iterator returned by the algorithm is pointing at the value 113
References