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 -1typedef 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 );}}
}