PAT A1155 Heap Paths （30 分）——完全二叉树，层序遍历，特定dfs遍历

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

 

#include <stdio.h> 
#include <algorithm>
#include <set>
#include <vector>
#include <string>
#include <iostream>
#include <queue>
using namespace std;
const int maxn=2001;
int tree[maxn] ;
int n;
vector<int> v;
void dfs(int st){
    v.push_back(tree[st]);
    if(st*2>n){
        if(st<=n){
            for(int i=0;i<v.size();i++){
                printf("%d%s",v[i],i!=v.size()-1?" ":"
");
            }
        }
    }
    else{
        //v.push_back(tree[st*2+1]);
        dfs(st*2+1);
        //v.pop_back();
        //v.push_back(tree[st*2]);
        dfs(st*2);
        
    }
    v.pop_back();
}
int main(){
    scanf("%d",&n);
    int ismax=1,ismin=1;
    for(int i=1;i<=n;i++){        
        scanf("%d",&tree[i]);        
    }
    dfs(1);
    for(int i=2;i<=n;i++){
        if(tree[i/2]>tree[i])ismin=0;
        if(tree[i/2]<tree[i])ismax=0;
    }
    if(ismin==1)printf("Min Heap
");
    else{
        printf("%s
",ismax==1?"Max Heap":"Not Heap");
    }

}

注意点：完全二叉树可以直接用数组存储，根节点下标为1，左子节点为2*root，右子节点2*root+1，当当前节点的左子节点编号大于n时，该节点即为叶节点。当节点下标大于n时，这个节点为空节点。

路径遍历用dfs实现，用一个vector控制路径上的值，每递归一次记得弹出