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>
#include <limits.h>

int A[2000001];
int N = 0;

void upheap(int k)
{
    int v = A[k];
    A[0] = INT_MAX;

    while(v > A[k / 2]){
        A[k] = A[k / 2];
        k = k / 2;
    }

    A[k] = v;
}

void insert(int v)
{
    A[++N] = v;
    upheap(N);
}

void downheap(int k)
{
    int j, v;
    v = A[k];

    while(k <= N / 2){
        j = k + k;
        if(j < N && A[j] < A[j + 1])
            j++;
        if(v >= A[j])
            break;
        A[k] = A[j];
        k = j;
    }

    A[k] = v;
}

int extract(void)
{
    int v = A[1];
    A[1] = A[N--];
    downheap(1);

    return v;
}

int main(void)
{
    char buf[126];
    int v;

    while(1){
        scanf("%s", buf);

        if(buf[0] == 'i'){
            scanf("%d", &v);
            insert(v);
        }else if(buf[1] == 'x'){
            printf("%d\n", extract());
        }else{
            break;
        }
    }

    return 0;
}