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+) * sizeof(ElementType));
     H->Size = ;
     H->Capacity = MaxSize;
     H->Elements[] = 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/] < item; i/= )
         H->Elements[i] = H->Elements[i/]; /* 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[]; /* 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=; Parent*<=H->Size; Parent=Child ) {
         Child = Parent * ;
         if( (Child!= H->Size) &&(H->Elements[Child] < H->Elements[Child+]) )
             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=;
     int *minheap=new int[n+];
     for(i=;i<=n;i++){
         scanf("%d",&temp);
         minheap[++size]=temp;
         for(j=size;j>=;j/=){
             if(temp<minheap[j/]){
                 minheap[j]=minheap[j/];
             }
             else{
                 break;
             }
         }
         minheap[j]=temp;
     }
     for(i=;i<m;i++){
         scanf("%d",&temp);
         while(temp){
             printf("%d",minheap[temp]);
             temp==?printf("\n"):printf(" ");
             temp/=;
         }
     }
     return ;
 }