題干：

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

題目大意：

按照標號給定一棵二叉樹，問你這是不是個堆，如果是，則是個大根堆還是小根堆。并讓你輸出所有的從根節點到葉子節點的路徑。

解題報告：

注意因為是二叉樹所以不需要建樹，用一個棧按照要求存儲路徑即可。最后按照路徑進行判斷是不是堆，是大根堆還是小根堆。

AC代碼：

#include<cstdio> #include<iostream> #include<algorithm> #include<queue> #include<stack> #include<map> #include<vector> #include<set> #include<string> #include<cmath> #include<cstring> #define FF first #define SS second #define ll long long #define pb push_back #define pm make_pair using namespace std; typedef pair<int,int> PII; const int MAX = 2e5 + 5; int n; int val[MAX]; vector<int> stk; vector<int> ans; void dfs(int idx) {if(idx * 2 > n) {int up = stk.size(),flag = 1;for(int i = 0; i<up; i++) {printf("%d%c",stk[i],i == up-1 ? '\n' : ' ');}//MAX 5 4 3 2 1for(int i = 1; i<up; i++) {if(stk[i] > stk[i-1]) flag = 0;}if(flag == 1) {ans.push_back(1); return;}//MIN 1 2 3 4 5flag = 1;for(int i = 1; i<up; i++) {if(stk[i] < stk[i-1]) flag = 0;}if(flag == 1) {ans.push_back(2); return;}ans.push_back(-1);return;}if(idx * 2 + 1 <= n) {stk.push_back(val[idx*2+1]);dfs(idx*2+1);stk.pop_back();}if(idx * 2 <= n) {stk.push_back(val[idx*2]);dfs(idx*2);stk.pop_back();} } int main() {cin>>n;for(int i = 1; i<=n; i++) scanf("%d",val+i);stk.push_back(val[1]);dfs(1);int Max = 1,Min = 1;for(auto x : ans) {if(x != 1) Max = 0;}for(auto x : ans) {if(x != 2) Min = 0;} if(Max == 1) printf("Max Heap\n");else if(Min == 1) printf("Min Heap\n");else printf("Not Heap\n");return 0 ; }

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