6-13 Percolate Up and Down（20 point(s)）

6-13 Percolate Up and Down（20 point(s)）

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

code：
void PercolateUp( int p, PriorityQueue H ){
	int i = p;
	int flag = 0;
	if(i==1)return;
	while(i!=1 && flag==0){
		if(H->Elements[i]<H->Elements[i/2]){//比父节点小，交换 
			int temp = H->Elements[i];
			H->Elements[i] = H->Elements[i/2];
			H->Elements[i/2] = temp;
		}
		else flag = 1;//否则不需要调整flag变1 
		i = i/2;//每次向上找父节点 
	}
	return; 
}
void PercolateDown( int p, PriorityQueue H ){
	int t;//记录较小元素下标，如果发现t和原来的没变则不用再继续调整了，如果t变成了原来的儿子下标，说明继续向下调整 
	int flag = 0;//标记是否需要继续调整
	int i = p;
	while(i*2<=H->Size&&flag==0){//注意！！i*2<=n才能进行下面的比较，如果单纯i<=n如果i=n，乘二肯定没有了 
		if(H->Elements[i]>H->Elements[i*2]){//比较当前点和左儿子的大小,如果现在元素大于左二子，则调整 
			t = i*2;
		}
		else//如果和左儿子比当前元素小，让t等于它本身 
		    t = i;
		if(i*2+1<=H->Size){//如果含有右儿子，则需要比较右儿子 
			if(H->Elements[t]>H->Elements[i*2+1]){//如果之前得到的最小的还比右儿子大
				t = i*2+1;//修改t的值 
			}
		}
		if(t==i){
			flag = 1;//如果t的值还是i本身则说明不需要继续调整了 
		}
		else{
			//交换
			int temp = H->Elements[i];
			H->Elements[i] = H->Elements[t];
			H->Elements[t] = temp; 
			i = t;//继续调整i值变成当前t 
		} 
	}
}