Sets are a type of associative containers in which each element has to be unique, because the value of the element identifies it. The value of the element cannot be modified once it is added to the set, though it is possible to remove and add the modified value of that element.

Pair is a simple container defined in **<utility>** header consisting of two data elements or objects.

- The first element is referenced as ‘first’ and the second element as ‘second’ and the order is fixed (first, second).
- Pair is used to combine together two values which may be different in type. Pair provides a way to store two heterogeneous objects as a single unit.
- Pair can be assigned, copied and compared. The array of objects allocated in a map or hash_map are of type ‘pair’ by default in which all the ‘first’ elements are unique keys associated with their ‘second’ value objects.
- To access the elements, we use variable name followed by dot operator followed by the keyword first or second.
- The pairs in a set are stored in sorted order, sorted by the key i.e. the first value of the pair.

**Sets of Pairs** help in performing the following operations:

- Add a pair, but do not allow duplicates.
- Remove pairs.
- Get count of distinct pairs.
- Check whether a pair is present in a set or not.

The **syntax** for creating sets of pairs is:

set<pair<datatype1, datatype2>>set_name;

### Creating Sets of Pairs

**Example:** Making pairs of all even numbers present in an array.

Input:2 3 1 6 5 8 10 9Output:(2, 6) (2, 8) (2, 10) (6, 8) (6, 10) (8, 10)Input:4 4 6 4Output:(4, 4) (4, 6)Input:24 24 24 24Output:(24, 24)Input:7, 100, 53, 81Output:No valid pair

Below program illustrate the solution to above problem:

In this example, range-base for loop is used with const reference for speed and security which iterates over all elements in the container. Variable ‘x’ is of type ‘pairs’. To access the elements of the pair, use variable name followed by dot operator followed by the keyword ‘first’ or ‘second’, these are public members of class pair.

**Program:**

`// C++ program to create Set of Pairs ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `typedef` `pair<` `int` `, ` `int` `> pairs; ` ` ` `// Constant reference ` `// reference for speed const to avoid changing values ` `void` `display(` `const` `set<pairs>& s) ` `{ ` ` ` `bool` `found = ` `false` `; ` ` ` ` ` `// range-based for loop ` ` ` `for` `(` `auto` `const` `&x : s) { ` ` ` `found = ` `true` `; ` ` ` `cout << ` `"("` `<< x.first << ` `", "` ` ` `<< x.second << ` `")"` ` ` `<< ` `" "` `; ` ` ` `} ` ` ` ` ` `if` `(not found) { ` ` ` `cout << ` `"No valid pair\n"` `; ` ` ` `} ` `} ` `int` `main() ` `{ ` ` ` `vector<` `int` `> v{ 2, 3, 1, 6, 8, 8, 10, 2 }; ` ` ` `set<pairs> s; ` ` ` ` ` ` ` ` ` `for` `(` `int` `i = 0; i < v.size() - 1; i++) { ` ` ` `for` `(` `int` `j = i + 1; j < v.size(); j++) { ` ` ` ` ` `// check for even number ` ` ` `if` `(v[i] % 2 == 0 && v[j] % 2 == 0) { ` ` ` ` ` `// makes pairs of even numbers ` ` ` `pairs x = make_pair(v[i], v[j]); ` ` ` ` ` `// inserts into the set ` ` ` `s.insert(x); ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` ` ` `// to display the pairs ` ` ` `display(s); ` ` ` ` ` `// to clear the set ` ` ` `s.clear(); ` `} ` |

*chevron_right*

*filter_none*

**Output:**

(2, 2) (2, 6) (2, 8) (2, 10) (6, 2) (6, 6) (6, 8) (6, 10) (8, 2) (8, 8) (8, 10) (10, 2) (10, 10)

## Recommended Posts:

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- Unordered Sets in C++ Standard Template Library
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- Sorting Vector of Pairs in C++ | Set 1 (Sort by first and second)
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- Find all pairs (a,b) and (c,d) in array which satisfy ab = cd
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- Count ordered pairs of positive numbers such that their sum is S and XOR is K
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- Number of special pairs possible from the given two numbers
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