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<string.h>

#define HEAP_SIZE 2000000
long int heap[HEAP_SIZE+1];
int heap_size;

void maxHeapify(long int heap[], int i)
{
	int l = i * 2;
	int r = i * 2 + 1;
	int largest;
	long int w;

	if((l <= heap_size) && (heap[l] > heap[i])){
		largest = l;
	}else{
		largest = i;
	}
	if((r <= heap_size) && (heap[r] > heap[largest])){
		largest = r;
	}
	if(largest != i){
		w = heap[i];
		heap[i] = heap[largest];
		heap[largest] = w;
		maxHeapify(heap, largest);
	}

	return;
}

void heapIncreaseKey(long int heap[], int i, long int key)
{
	int w;
	if(key < heap[i]){
		return;
	}
	heap[i] = key;
	while(i > 1 && heap[i / 2] < heap[i]){
		w = heap[i / 2];
		heap[i / 2] = heap[i];
		heap[i] = w;
		i = i / 2;
	}
	return;
}

void maxHeapInsert(long int heap[], long int key)
{
	heap_size = heap_size + 1;
	heap[heap_size] = -1;
	heapIncreaseKey(heap, heap_size, key);
	return;
}

long int heapExtractMax(long int heap[])
{
	long int max;
	if(heap_size < 1){
		return(-1);
	}
	max = heap[1];
	heap[1] = heap[heap_size];
	heap_size = heap_size - 1;
	maxHeapify(heap, 1);
	return(max);
}

int main()
{
	char cmd[30];
	long int key;

	do{
		scanf("%s", cmd);
		if(strcmp("insert", cmd) == 0){
			scanf("%ld", &key);
			maxHeapInsert(heap, key);
		}else if(strcmp("extract", cmd) == 0){
			printf("%ld\n", heapExtractMax(heap));
		}
	}while(strcmp("end", cmd) != 0);

	return(0);
}