1155 Heap Paths（31行代码+详细注释）

分数 30

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作者 陈越

单位 浙江大学

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 (1int), 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

代码长度限制

16 KB

时间限制

400 ms

内存限制

64 MB

#include
using namespace std;
const int N=1009,INF=0x3f3f3f3f;
int n; 
int tree[N];
vectorpath;
int big,small;
void dfs(int u){
    path.push_back(tree[u]);//加入该结点 
    if(2*u>n){//若为叶结点则输出路径 
        cout<         for(int i=1;i             cout<<' '<             if(path[i]<=path[i-1])big=1;
            else if(path[i]>=path[i-1])small=1;
        }
        cout<     }
    if(2*u+1<=n)dfs(2*u+1);//递归右孩子 
    if(2*u<=n)dfs(2*u);//递归左孩子 
    path.pop_back();//恢复现场 
}
int main(){
    #ifdef ONLINE_JUDGE  
    #else
        freopen("1.txt","r",stdin);
    #endif
    cin>>n;
    for(int i=1;i<=n;i++)cin>>tree[i];//输入 
    dfs(1);//深搜 
    if(big&&small)cout<<"Not Heap"<     else if(big)cout<<"Max Heap"<     else cout<<"Min Heap"<     return 0;
}