PAT Advanced 1155 Heap Paths (30 分)

Posted 2022-12-13 littlepage

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree. (Quoted from Wikipedia at https://en.wikipedia.org/wiki/Heap_(data_structure))

One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order.

Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (1), the number of keys in the tree. Then the next line contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree.

Output Specification:

For each given tree, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree.

Finally print in a line Max Heap if it is a max heap, or Min Heap for a min heap, or Not Heap if it is not a heap at all.

Sample Input 1:

8
98 72 86 60 65 12 23 50

Sample Output 1:

98 86 23
98 86 12
98 72 65
98 72 60 50
Max Heap

Sample Input 2:

8
8 38 25 58 52 82 70 60

Sample Output 2:

8 25 70
8 25 82
8 38 52
8 38 58 60
Min Heap

Sample Input 3:

8
10 28 15 12 34 9 8 56

Sample Output 3:

10 15 8
10 15 9
10 28 34
10 28 12 56
Not Heap

#include <iostream>
#include <vector>
using namespace std;
int n,heap[1010];bool isMin=1,isMax=1;
vector<int> v;
/**思路：先序遍历的镜像表示直接打印*/
void dfs(int index)
    if(index*2>n && index*2+1>n)
        if(index<=n)
            for(int i=0;i<v.size();i++)
                printf("%d%s",v[i],i!=v.size()-1?" ":"\n");
            
    else
        v.push_back(heap[index*2+1]);
        dfs(index*2+1);
        v.pop_back();
        v.push_back(heap[index*2]);
        dfs(index*2);
        v.pop_back();
    

int main()

    cin>>n;
    for(int i=1;i<=n;i++) cin>>heap[i];
    v.push_back(heap[1]);
    dfs(1);
    /**判断父亲是否都比孩子大或者小*/
    for(int i=2;i<=n;i++)
        if(heap[i/2]>heap[i]) isMin=0;
        if(heap[i/2]<heap[i]) isMax=0;
    
    if(isMin==1) printf("Min Heap");
    else if(isMax==1) printf("Max Heap");
    else printf("Not Heap");
    system("pause");
    return 0;