Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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 N 2000000
#define INF -1000000

int size, A[N];

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

void maxHeapify(int i) {
	int l,r,largest;
	int tmp;

	l = i*2;
	r = i*2+1;

	if (l <= size && A[l] > A[i]) largest = l;
	else largest = i;
	if (r <= size && A[r] > A[largest]) largest = r;

	if (largest != i) {
		tmp = A[i];
		A[i] = A[largest];
		A[largest] = tmp;
		maxHeapify(largest);
	}
}

void insert(int key) {
	size++;
	A[size] = INF;
	increaseKey(size, key);
}

int extract() {
	int max;
	if (size < 1) return INF;
	max = A[1];
	A[1] = A[size--];
	maxHeapify(1);
	return max;
}

int main() {
	int k;
	char com[10];

	while (1) {
		scanf("%s", com);
		if (com[0] == 'e' && com[1] == 'n') break;
		if (com[0] == 'i') {
			scanf("%d", &k);
			insert(k);
		} else {
			printf("%d\n", extract());
		}
	}

	return 0;
}