pta Percolate Up and Down（最小堆的插入维护和删除维护）

Write the routines to do a “percolate up” and a “percolate down” in a binary min-heap.
Format of functions:

void PercolateUp( int p, PriorityQueue H );
void PercolateDown( int p, PriorityQueue H );

where int p is the position of the element, and PriorityQueue is defined as the following:

typedef struct HeapStruct *PriorityQueue;
struct HeapStruct {
    ElementType  *Elements;
    int Capacity;
    int Size;
};

Sample program of judge:

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

typedef int ElementType;
#define MinData -1

typedef struct HeapStruct *PriorityQueue;
struct HeapStruct {
    ElementType  *Elements;
    int Capacity;
    int Size;
};

PriorityQueue Initialize( int MaxElements ); /* details omitted */

void PercolateUp( int p, PriorityQueue H );
void PercolateDown( int p, PriorityQueue H );

void Insert( ElementType X, PriorityQueue H ) 
{
    int p = ++H->Size;
    H->Elements[p] = X;
    PercolateUp( p, H );
}

ElementType DeleteMin( PriorityQueue H ) 
{ 
    ElementType MinElement; 
    MinElement = H->Elements[1];
    H->Elements[1] = H->Elements[H->Size--];
    PercolateDown( 1, H );
    return MinElement; 
}

int main()
{
    int n, i, op, X;
    PriorityQueue H;

    scanf("%d", &n);
    H = Initialize(n);
    for ( i=0; i<n; i++ ) {
        scanf("%d", &op);
        switch( op ) {
        case 1:
            scanf("%d", &X);
            Insert(X, H);
            break;
        case 0:
            printf("%d ", DeleteMin(H));
            break;
        }
    }
    printf("\nInside H:");
    for ( i=1; i<=H->Size; i++ )
        printf(" %d", H->Elements[i]);
    return 0;
}

/* Your function will be put here */

Sample Input:

9
1 10
1 5
1 2
0
1 9
1 1
1 4
0
0

Sample Output:

2 1 4 
Inside H: 5 10 9

思路：
题目让实现最小堆的插入维护和删除维护。只要记住最小的在上面就行。
另外要注意down的时候可能只有一个儿子。

代码：

void PercolateDown( int p, PriorityQueue H )
{   
    if(p<<1 > H->Size)return;

    int replace;
    if(p<<1+1 <= H->Size)replace = (H->Elements[p<<1] < H->Elements[p<<1+1] ? p<<1 : p<<1+1);
    else replace = p<<1;
    if(H->Elements[replace] < H->Elements[p])
    {
        int mid = H->Elements[replace];
        H->Elements[replace] = H->Elements[p];
        H->Elements[p] = mid;
        PercolateDown( replace, H );
    }
}

void PercolateUp( int p, PriorityQueue H )
{
    if(p == 1)return;

    if(p&1)
    {
        if(H->Elements[(p-1)>>1] > H->Elements[p])
        {
            int mid = H->Elements[(p-1)>>1];
            H->Elements[(p-1)>>1] = H->Elements[p];
            H->Elements[p] = mid;
            PercolateUp( (p-1)>>1, H );
        }
    }
    else
    {
        if(H->Elements[p>>1] > H->Elements[p])
        {
            int mid = H->Elements[p>>1];
            H->Elements[p>>1] = H->Elements[p];
            H->Elements[p] = mid;
            PercolateUp( p>>1, H );
        }
    }
}