heap 堆的各类操作

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

int N;
//最小堆
int heap[20];

//交换两个元素的值

void swap( int &x, int &y)
{
    int temp;
    temp = x;
    x = y;
    y = temp;
}

// 非递归写法
void down ( int x )
{
    int i, j, flag = 1;
    if ( 2 * x <= N) {
        while (flag && (i = 2 * x) <= N )
        {
            if ( i + 1 <= N && heap[i] > heap[i+ 1] )
                i++;
            if ( heap[x] > heap[i])
                swap(heap[x],heap[i]), x = i;
            else
                flag = 0;
        }
            
    }
}

// 递归写法

void down_x ( int x)
{
    int i = 2 * x;
    if ( i <= N ) {
        if ( i + 1 <= N && heap[i] > heap[i+1])
            i++;
        if (heap[x] > heap[i]) {
            swap(heap[x],heap[i]);
            down(i);
        }
    }
}

//上移，非递归
void up( int x )
{
    int  flag = 1;
    while ( x > 1 && flag )
    {
        if ( heap[x] < heap[x / 2]) {
            swap(heap[x],heap[x / 2]);
            x = x / 2;
        }
        else
            flag = 0;
    }
    
}


//上移，递归
void up_x( int x)
{
    if (x > 1 && heap[x] < heap[x/2]) {
        swap(heap[x],heap[x/2]);
        up( x / 2);
    }
}

//建堆
void makeheap(int x)
{
    int i;
    for(i = x / 2; i; i--)
        down_x(i);
}

//从小到大输出
void heap_sort( )
{
    int i;
    for ( i = N; i; i--) {
         printf("%d ",heap[1]);
        swap(heap[i], heap[1]);
        N--;
        down_x(1);
    }
}
    
int pop(  )
{
    swap(heap[1],heap[N--]);
    down(1);
    return heap[N + 1];
}

int main( )
{
    int i, j;
    scanf("%d",&N);
    j = N;
    for (i = 1; i <= N; i++) {
        scanf("%d",&heap[i]);
          up(i);
    }
    //makeheap(N);
    //heap_sort( );
    for (i = 0; i < j; i++)
        printf("%d ",pop( ));
    return 0;
}