#include <stdio.h>
#include <stdlib.h>

/*

MAX-HEAPIFY(A, i)     //保持最大堆
 1 l ← LEFT(i)
 2 r ← RIGHT(i)
 3 if l ≤ heap-size[A] and A[l] > A[i]
 4    then largest ← l
 5    else largest ← i
 6 if r ≤ heap-size[A] and A[r] > A[largest]
 7    then largest ← r
 8 if largest ≠ i
 9    then exchange A[i] <-> A[largest]
10         MAX-HEAPIFY(A, largest) 
*/
void maxheap(int A[], int len, int i)
{
    int l = 2*i+1;
    int r = 2*i+2;

    int largest = i;

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

    if(r < len && A[r] > A[largest])
        largest = r;

    if (largest != i){
        int tmp = A[largest];
        A[largest] = A[i];
        A[i] = tmp;
        maxheap(A, len, largest);
    }

}

void minheap(int A[], int len, int i)
{
    int l = 2*i+1;
    int r = 2*i+2;

    int smallest = i;

    if(l < len && A[l] < A[i])
        smallest = l;
    else
        smallest = i;

    if(r < len && A[r] < A[smallest])
        smallest = r;

    if (smallest != i){
        int tmp = A[smallest];
        A[smallest] = A[i];
        A[i] = tmp;
        minheap(A, len, smallest);
    }

}
/*
BUILD-MAX-HEAP(A)  //建堆
1  heap-size[A] ← length[A]
2  for i ← |_length[A]/2_| downto 1
3       do MAX-HEAPIFY(A, i) 
*/
void buildheap(int A[], int len)
{
    int heapsize = len;
    for(int i = len/2-1; i >=0; i--)
        //maxheap(A,len,i);
        minheap(A,len,i);
}


/*
HEAPSORT(A)    //n-1次調用MAX-HEAPIFY，所以，O（n*lgn）
1 BUILD-MAX-HEAP(A)      //建最大堆，O（n）
2 for i ← length[A] downto 2
3    do exchange A[1] <-> A[i]
4       heap-size[A] ← heap-size[A] - 1
5       MAX-HEAPIFY(A, 1)    //保持堆的性質，O（lgn） 
*/
void heapsort(int A[], int len)
{

    buildheap(A,len);
    for(int i = len-1; i>=1; i--){
        int tmp = A[0];
        A[0] = A[i];
        A[i] = tmp;

        len = len-1;
        minheap(A,len,0);
    }
}
int main()
{
    int A[] = {1,5,4,7,9,2,3,6,8}; 

    int len = sizeof(A)/sizeof(A[0]);

    for(int i = 0; i < len ; i++)
        printf("%d ", A[i]);

    printf("\n");
    //buildheap(A,len);
    heapsort(A,len);
    for(int i = 0; i < len ; i++)
        printf("%d ", A[i]);

    printf("\n");
    return 1;
}