PAT 1155 Heap Paths (30分)

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:

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

先右后左的输出路径，并判断是否是大顶堆还是小顶堆还是不是堆 

#include <bits/stdc++.h>
#define Max 1100
using namespace std;
int n, a[Max];
vector<int> vec;
void dfs(int i) {
  if( 2*i+1 >= n && 2*i+2 >= n){
    if(i < n) {
      for(int j = 0; j < vec.size(); j++) {
        cout << vec[j];
        if(j != vec.size() - 1) cout << " ";
        else cout << endl;
      }
    }
  }else {
//    cout << a[2*i+2] << "  " << 2*i+2<< endl;
    vec.push_back(a[2*i+2]);
    dfs(2*i + 2);
    vec.pop_back();
    
    vec.push_back(a[2*i+1]);
    dfs(2*i + 1);
    vec.pop_back();
  }
}

//判断大顶堆
bool isMaxHeap(int a[]) {
  int flag = 0;
  for(int i = 0; i < n; i++) {
    int c1 = 2 * i + 1;
    int c2 = 2 * i + 2;
    if(c1 < n) {
      if(a[i] >= a[c1])
        continue;
      else flag = 1;
    }
    if(c2 < n) {
      if(a[i] >= a[c2])
        continue;
      else flag = 1;
    }
  }
  return !flag;
}
//判断小顶堆
bool isMinHeap(int a[]) {
  int flag = 0;
  for(int i = 0; i < n; i++) {
    int c1 = 2 * i + 1;
    int c2 = 2 * i + 2;
    if(c1 < n) {
      if(a[i] <= a[c1])
        continue;
      else flag = 1;
    }
    if(c2 < n) {
      if(a[i] <= a[c2])
        continue;
      else flag = 1;
    }
  }
  return !flag;
}
int main() {
  cin >> n;
  for(int i = 0; i < n; i++) 
    cin >> a[i];
  vec.clear();  
  vec.push_back(a[0]);
  dfs(0);
  if(isMaxHeap(a)) {
    cout << "Max Heap" << endl; 
  }else if(isMinHeap(a)) {
    cout << "Min Heap" << endl;
  }else cout << "Not Heap" << endl;
  return 0;
}