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

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:

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


首先涉及了一些堆的思想，但是用来用去还是当成树来用。
二叉树都已经写好了，然后从最右边的节点路径输出来。

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 int n;
 4 int an[2005];
 5 bool isbig = true, islittle = true;
 6 vector<int> v;
 7 void dfs(int x){
 8     if(x*2 > n && x*2+1 > n){
 9         for(int i = 0; i < v.size(); i++){
10             printf("%d%c", v[i], i == v.size()-1?'
':' ');
11         }
12     }else{
13         if(x*2+1 <= n){
14             v.push_back(an[x*2+1]);
15             dfs(x*2+1);
16             v.pop_back();
17         }
18         if(x*2 <= n){
19             v.push_back(an[x*2]);
20             dfs(x*2);
21             v.pop_back();
22         }
23     }
24 }
25 
26 int main(){
27     cin >> n;
28     for(int i = 1 ; i <= n ; ++i){
29         cin >> an[i];
30         if(i >= 2){
31             if(an[i/2] < an[i]) isbig = false;
32             if(an[i/2] > an[i]) islittle = false;
33         }
34     }
35     v.push_back(an[1]);
36     dfs(1);
37     if(isbig){
38         puts("Max Heap");
39     }else if(islittle){
40         puts("Min Heap");
41     }else{
42         puts("Not Heap");
43     }
44     return 0;
45 }