A1155

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<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:

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<bits/stdc++.h>
using namespace std;
int heap[1004],N,ismax=1,ismin=1;
vector<int>v;
void MirrPreOrder(int root,vector<int>&temp){
    if(root>N)return;
    temp.push_back(heap[root]);
    if(2*root>N){
        for(int i=0;i<v.size();i++){
            if(i){
                printf(" ");
                if(temp[i]<temp[i-1])ismin=0;
                if(temp[i]>temp[i-1])ismax=0;
            }
            printf("%d",v[i]);
        }
        printf("\n");
    }
    MirrPreOrder(2*root+1,temp);
    MirrPreOrder(2*root,temp);
    temp.pop_back();
}
int main(){
    cin>>N;
    for(int i=1;i<=N;i++)
        scanf("%d",&heap[i]);
    MirrPreOrder(1,v);
    if(ismin)cout<<"Min Heap";
    else if(ismax)cout<<"Max Heap";
    else cout<<"Not Heap";
    return 0;
}

A1155

1155 Heap Paths (30分)

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