PAT Advanced 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), 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 <the iostream> 
#include <Vector>
 the using  namespace STD;
 int n-, heap [ 1010 ]; BOOL isMin = . 1 , isMax = . 1 ; 
Vector < int > V;
 / * * ideas: preorder traversal of a direct print image * / 
void DFS ( int index) {
     IF (index * 2 > n-index && * 2 + . 1 > n-) {
         IF (index <= n-)
             for ( int I = 0 ; I <v.size (); I ++ ) {
                printf("%d%s",v[i],i!=v.size()-1?" ":"\n");
            }
    }else{
        v.push_back(heap[index*2+1]);
        dfs(index*2+1);
        v.pop_back();
        v.push_back(heap[index*2]);
        dfs(index*2);
        v.pop_back();
    }
}
int main()
{
    CIN>> n-;
     for ( int I = . 1 ; I <= n-; I ++) >> CIN heap [I]; 
    v.push_back (heap [ . 1 ]); 
    DFS ( . 1 );
     / * * is determined whether or not the father than children larger or smaller * / 
    for ( int I = 2 ; I <= n-; I ++ ) {
         IF (heap [I / 2 ]> heap [I]) isMin = 0 ;
         IF (heap [I / 2 ] <heap [I ]) isMax = 0 ; 
    } 
    IF (isMin == . 1 ) the printf ( " Min Heap " );
    else if(isMax==1) printf("Max Heap");
    else printf("Not Heap");
    system("pause");
    return 0;
}