04-树9. Path in a Heap (25)

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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 areseparated by a space, and there must be no extra space at the end of the line.

Sample Input:

5 346 23 26 24 105 4 3

Sample Output:

24 23 1046 23 1026 10

提交代码

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这个题目和云课堂上面讲的一样的。

主要涉及的知识点为。

1，堆的创建——最小堆，利用数组来表示。和上面一道题很类似。下标为i 的节点的左右儿子节点的小标为2*i 和2*i+1，反过来，父亲下标为i/2.

2，插入一个节点。先放在最后面，然后和父亲比较，如果不符合的话，换。

3，索引值的理解。从1开始，在0处放上一个哨兵。最小堆上面的哨兵的值为最小值。

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代码如下。

#include <iostream>#include <stdlib.h>using namespace std;/* run this program using the console pauser or add your own getch, system("pause") or input loop */typedef struct MinHeap{int *data;int size;int cap;}* pMinHeap;pMinHeap Creat(int Size){pMinHeap h =(pMinHeap)malloc(sizeof(struct MinHeap));h->data=(int *)malloc((Size+1)*sizeof(int));h->cap=Size;h->size=0;h->data[0]=-10001;//The Max datareturn h;}void Insert(pMinHeap h, int d){if(h->size == h->cap)return;int i=++h->size;for(;h->data[i/2]>d; i/=2){h->data[i]=h->data[i/2];}h->data[i]=d;}int main(int argc, char** argv) {int N=0, M=0;pMinHeap H;cin>>N>>M;H=Creat(N);for(int i=0; i<N; i++){int tmp=0;cin>>tmp;Insert(H,tmp);}for(int i=0; i<M; i++){int index=0;cin>>index;for(int j=index; j>0; j/=2){cout<<H->data[j];j==1?cout<<endl:cout<<" ";}}return 0;}

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