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>

int h, A[2000001];

void maxHeapify(int i) {
	int temp;
	int l,r,largest;
	l = 2*i;
	r = 2*i+1;

	if(l<=h && A[l] > A[i]) largest = l;
	else largest = i;
	if(r<=h && A[r]>A[largest]){ largest = r; }
	if(largest != i){
		temp = A[i];
		A[i] = A[largest];
		A[largest] = temp;
		maxHeapify(largest);
	} 
}

int extract() {
	int maxv;
	if (h < 1) return;
	maxv = A[1];
	A[1] = A[h--];
	maxHeapify(1);
	return maxv;
}

void increaseKey(int i, int key) {
	int temp;
	if (key < A[i]) return;
	A[i] = key;
	while (i>1 && A[i/2]<A[i]) {
		temp = A[i];
		A[i] = A[i/2];
		A[i/2] = temp;
		i = i/2;
	}
}

void insert(int key) {
	h++;
	A[h] = -1000000000;
	increaseKey(h, key);
}

main() {
	int key;
	char com[20];
	while (1) {
		scanf("%s", com);
		if (com[0] == 'i') {
			scanf("%d", &key);
			insert(key);
		}
		else if (strcmp(com, "extract") == 0) {
			printf("%d\n", extract());
		}
		else break;
	}

	return 0;
}