1147 Heaps (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))

Your job is to tell if a given complete binary tree is a heap.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers: M ( $\leq 100), the number of trees to be tested; and N (1 < N \leq 1,000), the number of keys in each tree, respectively. Then M lines follow, each contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree.$

Output Specification:

For each given tree, 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. Then in the next line print the tree's postorder traversal sequence. All the numbers are separated by a space, and there must no extra space at the beginning or the end of the line.

Sample Input:

3 8
98 72 86 60 65 12 23 50
8 38 25 58 52 82 70 60
10 28 15 12 34 9 8 56

Sample Output:

Max Heap
50 60 65 72 12 23 86 98
Min Heap
60 58 52 38 82 70 25 8
Not Heap
56 12 34 28 9 8 15 10

依然是堆的性质，再加一个后序遍历，这题30分有点多

 1 #include <bits/stdc++.h>
 2 
 3 using namespace std;
 4 int an[1005];
 5 int n,m;
 6 vector<int> v;
 7 
 8 void predfs(int x){
 9     if(x*2 <= m)
10         predfs(x*2);
11     if(x*2+1 <= m)
12         predfs(x*2+1);
13     v.push_back(an[x]);
14 }
15 
16 int main(){
17     cin >> n >> m;
18     while(n--){
19         v.clear();
20         bool isbig = true, islittle = true;
21         for(int i = 1 ; i <= m ; ++i){
22             cin >> an[i];
23             if(i > 2){
24                 if(an[i/2] < an[i]) isbig = false;
25                 if(an[i/2] > an[i]) islittle = false;
26             }
27         }
28         if(isbig)
29             puts("Max Heap");
30         else if(islittle)
31             puts("Min Heap");
32         else
33             puts("Not Heap");
34         predfs(1);
35         for(int i = 0 ; i < v.size(); ++i)
36             printf("%d%c",v[i], i == v.size()-1? '
':' ');
37     }
38 
39     return 0;
40 }