Problem:
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Priority Queue

A priority queue is a data structure which maintains a set $S$ of elements, each of with an associated value (key), and supports the following operations:

$insert(S, k)$: insert an element $k$ into the set $S$

$extractMax(S)$: remove and return the element of $S$ with the largest key

Write a program which performs the $insert(S, k)$ and $extractMax(S)$ operations to a priority queue $S$.
The priority queue manages a set of integers, which are also keys for the priority.

Input

Multiple operations to the priority queue $S$ are given. Each operation is given by "insert $k$", "extract" or "end" in a line. Here, $k$ represents an integer element to be inserted to the priority queue.

The input ends with "end" operation.

Output

For each "extract" operation, print the element extracted from the priority queue $S$ in a line.

Constraints

The number of operations $\leq 2,000,000$

$0 \leq k \leq 2,000,000,000$

Sample Input 1

insert 8
insert 2
extract
insert 10
extract
insert 11
extract
extract
end

Sample Output 1

8
10
11
2

Solution in C (judge verdict: Accepted)

#include <stdio.h>
#define INF 2000000001
int heap[1000000];
int size;

void insert(int);
void heapIncreaseKey(int);
int extractMax();
void maxHeapify(int);
int main (){
    int i,tmp;
    char com[10];
    size=0;
    while(1){
        scanf("%s",com);
        if(com[0]=='i'){
            scanf("%d",&tmp);
            insert(tmp);
        }
        else if(com[1]=='x'){
            printf("%d\n",extractMax());
        }
        else break;
    }
    return 0;
}
void insert(int key){
    size++;
    heap[size]=-INF;
    heapIncreaseKey(key);
}
void heapIncreaseKey(int key){
    int i,tmp;
    i=size;
    heap[i]=key;
    while(i>1 && heap[i/2]<heap[i]){
        tmp=heap[i];
        heap[i]=heap[i/2];
        heap[i/2]=tmp;
        i=i/2;
    }
}
int extractMax(){
    int max;
    max=heap[1];
    heap[1]=heap[size];
    size--;
    maxHeapify(1);
    return max;
}
void maxHeapify(int i){
    int l,r,largest,tmp;
    l=i*2;
    r=i*2+1;
    if(l<=size && heap[l]>heap[i]){
        largest=l;
    }
    else{
        largest=i;
    }
    if(r<=size && heap[r]>heap[largest]){
        largest=r;
    }
    if(largest!=i){
        tmp=heap[i];
        heap[i]=heap[largest];
        heap[largest]=tmp;
        maxHeapify(largest);
    }
}