PAT-A 真题 – 1155 Heap Paths

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 $N$ ( $1 < N \leq 1, 000$ ), 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

题目大意：给出一个堆的中序序列，从右到左输出堆从上到下的路径，然后判断是大顶堆还是小顶堆还是非堆。

这道题dfs就可以了，输出路径，可以使用vector模拟一个栈，到达叶子节点就把栈内元素输出一遍。

#include <bits/stdc++.h>
using namespace std;

bool flag = true, is_maxheap;
vector<int> H, stk;

void output(){
  for(int i = 0; i < stk.size(); i++){
    if(i){
      cout << ' ';
      if((stk[i] <= stk[i - 1]) != is_maxheap)
        flag = false;
    } 
    cout << stk[i];
  }
  cout << endl;
}

void dfs(int idx){
  stk.push_back(H[idx]);
  if(idx * 2 >= H.size())  //叶子节点 
    output();
  else{
    if(idx * 2 + 1 < H.size())
      dfs(idx * 2 + 1);
    dfs(idx * 2);
  }
  stk.pop_back();
}

int main(){
  int cnt;
  cin >> cnt;
  H.resize(cnt + 1);
  for(int i = 1; i <= cnt; i++)
    cin >> H[i];
  if(H[1] < H[2]) is_maxheap = false;
  else is_maxheap = true;
  dfs(1);
  if(flag){
    if(is_maxheap) cout << "Max Heap\n";
    else cout << "Min Heap\n";
  }
  else cout << "Not Heap\n";
  return 0;
}

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