pat04-树9. Path in a Heap (25)

04-树9. Path in a Heap (25)

时间限制

150 ms

内存限制

65536 kB

代码长度限制

8000 B

判题程序

Standard

作者

CHEN, Yue

Insert a sequence of given numbers into an initially empty min-heap H. Then for any given index i, you are supposed to print the path from H[i] to the root.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers N and M (<=1000) which are the size of the input sequence, and the number of indices to be checked, respectively. Given in the next line are the N integers in [-10000, 10000] which are supposed to be inserted into an initially empty min-heap. Finally in the last line, M indices are given.

Output Specification:

For each index i in the input, print in one line the numbers visited along the path from H[i] to the root of the heap. The numbers are separated by a space, and there must be no extra space at the end of the line.

Sample Input:

5 3
46 23 26 24 10
5 4 3

Sample Output:

24 23 10
46 23 10
26 10

---

提交代码

关于堆的操作（以大顶堆为例）：

1.建堆。

MaxHeap Create( int MaxSize )
{ /* 创建容量为MaxSize的空的最大堆 */
    MaxHeap H = malloc( sizeof( struct HeapStruct ) );
    H->Elements = malloc( (MaxSize+1) * sizeof(ElementType));
    H->Size = 0;
    H->Capacity = MaxSize;
    H->Elements[0] = MaxData;
/* 定义“哨兵”为大于堆中所有可能元素的值，便于以后更快操作 */
    return H;
}

2.插入。

void Insert( MaxHeap H, ElementType item )
{ /* 将元素item 插入最大堆H， 其中H->Elements[0]已经定义为哨兵 */
    int i;
    if ( IsFull(H) ) {
        printf("最大堆已满");
        return;
    }
    i = ++H->Size; /* i指向插入后堆中的最后一个元素的位置 */
    for ( ; H->Elements[i/2] < item; i/=2 )
        H->Elements[i] = H->Elements[i/2]; /* 向下过滤结点 */
    H->Elements[i] = item; /* 将item 插入 */
} 

3.删除最大值。

ElementType DeleteMax( MaxHeap H )
{ /* 从最大堆H中取出键值为最大的元素， 并删除一个结点 */
    int Parent, Child;
    ElementType MaxItem, temp;
    if ( IsEmpty(H) ) {
        printf("最大堆已为空");
        return;
    }
    MaxItem = H->Elements[1]; /* 取出根结点最大值 */
/* 用最大堆中最后一个元素从根结点开始向上过滤下层结点 */
    temp = H->Elements[H->Size--];
    for( Parent=1; Parent*2<=H->Size; Parent=Child ) {
        Child = Parent * 2;
        if( (Child!= H->Size) &&(H->Elements[Child] < H->Elements[Child+1]) )
            Child++; /* Child指向左右子结点的较大者 */
        if( temp >= H->Elements[Child] ) break;
        else /* 移动temp元素到下一层 */
        H->Elements[Parent] = H->Elements[Child];
    }
    H->Elements[Parent] = temp;
    return MaxItem;
}

代码如下：

#include<cstdio>
#include<algorithm>
#include<iostream>
#include<cstring>
#include<queue>
#include<vector>
#include<map>
#include<string>
using namespace std;
int main(){
    //freopen("D:\INPUT.txt","r",stdin);
    int n,m;
    scanf("%d %d",&n,&m);
    int i,j,temp,size=0;
    int *minheap=new int[n+1];
    for(i=1;i<=n;i++){
        scanf("%d",&temp);
        minheap[++size]=temp;
        for(j=size;j>=2;j/=2){
            if(temp<minheap[j/2]){
                minheap[j]=minheap[j/2];
            }
            else{
                break;
            }
        }
        minheap[j]=temp;
    }
    for(i=0;i<m;i++){
        scanf("%d",&temp);
        while(temp){
            printf("%d",minheap[temp]);
            temp==1?printf("
"):printf(" ");
            temp/=2;
        }
    }
    return 0;
}