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Priority queue of pairs in C++ with ordering by first and second element
• Difficulty Level : Medium
• Last Updated : 28 Jul, 2020

Priority Queue: Priority queue is the extension of the queue in which elements associated with priority and elements having higher priority is popped first.

Priority queue can contain elements with various data types such as integer, pair of integers, custom data type. But one thing is common that there is one element that defines the priority of the element.
Therefore, the Priority queue of pairs can have two types of ordering –

• Ordered by the first element of pair
• Ordered by the second element of pair

### Priority Queue ordered by first element

In C++ if the element is in the form of pairs, then by default the priority of the elements is dependent upon the first element. Therefore, we just have to use the priority queue of pairs only.

## C++

 // C++ implementation of the// priority queue of pairs// ordered by the first element  #include #include using namespace std;  // Function to print the data of// the priority queue ordered by firstvoid showpq(    priority_queue > g){    // Loop to print the elements    // until the priority queue    // is not empty    while (!g.empty()) {        cout << g.top().first             << " " << g.top().second             << endl;        g.pop();    }    cout << endl;}  // Driver Codeint main(){    priority_queue > p1;      // Insertion of elements    p1.push(make_pair(4, 5));    p1.push(make_pair(5, 4));    p1.push(make_pair(1, 6));    p1.push(make_pair(7, 3));    p1.push(make_pair(9, 4));    showpq(p1);    return 0;}
Output:
9 4
7 3
5 4
4 5
1 6

Note: If the first element of some pairs will be same, then the comparison will be made on the basis of the second element.

### Priority Queue ordered by second element (Max)

The idea is to use structure with the concept of the operator overloading in the priority queue for ordering the pairs by its second element.

Below is the implementation of the priority queue ordered by second element –

## C++

 // C++ implementation of the// priority queue in which elements// are sorted by the second element  #include #include #include   using namespace std;  typedef pair pd;  // Structure of the condition// for sorting the pair by its// second elementsstruct myComp {    constexpr bool operator()(        pair const& a,        pair const& b)        const noexcept    {        return a.second < b.second;    }};  // Function to show the elements// of the priority queuevoid showpq(    priority_queue, myComp>        g){    // Loop to print the elements    // until the priority queue    // is not empty    while (!g.empty()) {        cout << g.top().first             << " " << g.top().second             << endl;        g.pop();    }    cout << endl;}  // Driver Codeint main(){    priority_queue, myComp> p1;    p1.push(make_pair(4, 5));    p1.push(make_pair(5, 4));    p1.push(make_pair(1, 6));    p1.push(make_pair(7, 3));    p1.push(make_pair(9, 4));      // Function Call    showpq(p1);    return 0;}
Output:
1 6
4 5
9 4
5 4
7 3

### Priority queue ordered by second element (Min)

The idea is to use the operator overloading to implement the priority queue ordered by its second element with the minimum element at the top.

Below is the implementation of the priority queue:

## C++

 // C++ implementation of the priority// queue sorted by the second element// in the decreasing order  #include #include #include   using namespace std;  typedef pair pd;  // Structure of the operator// overloading for comparisonstruct myComp {    constexpr bool operator()(        pair const& a,        pair const& b)        const noexcept    {        return a.second > b.second;    }};  // Function to print the elements// of the priority queuevoid showpq(    priority_queue, myComp> g){    // Loop to print the elements    // of the priority queue    while (!g.empty()) {        cout << g.top().first             << " " << g.top().second             << endl;        g.pop();    }    cout << endl;}  // Driver Codeint main(){    priority_queue, myComp> p1;      // Insertion of the elements    p1.push(make_pair(4, 5));    p1.push(make_pair(5, 4));    p1.push(make_pair(1, 6));    p1.push(make_pair(7, 3));    p1.push(make_pair(9, 4));    showpq(p1);    return 0;}
Output:
7 3
5 4
9 4
4 5
1 6
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