1155 Heap Paths (30分)

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<N≤1,000), 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;

const int N=1010;

int n;
int h[N];
bool gt,lt;
vector<int> path;

void dfs(int u)
{
path.push_back(h[u]);
    if (u * 2 > n)  // 叶节点
    {
        cout << path[0];
        for (int i = 1; i < path.size(); i ++ )
        {
            cout << ' ' << path[i];
            if (path[i] > path[i - 1]) gt = true;
            else if (path[i] < path[i - 1]) lt = true;
        }
        cout << endl;
    }

    if (u * 2 + 1 <= n) dfs(u * 2 + 1);
    if (u * 2 <= n) dfs(u * 2);

    path.pop_back();  //递归弹出 

}

int main()
{
    cin>>n;
    for(int i=1;i<=n;i++) cin>>h[i];

    dfs(1);


    if(gt&&lt) cout<<"Not Heap"<<endl;
    else if(gt) cout<<"Min Heap"<<endl;
    else cout<<"Max Heap"<<endl;

    return 0;
}