PAT 1147 Heaps (30分)

1147 Heaps (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​​))

Your job is to tell if a given complete binary tree is a heap.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers: M (≤ 100), the number of trees to be tested; and N (1 < N ≤ 1,000), the number of keys in each tree, respectively. Then M lines follow, each 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, 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. Then in the next line print the tree's postorder traversal sequence. All the numbers are separated by a space, and there must no extra space at the beginning or the end of the line.

Sample Input:

3 8
98 72 86 60 65 12 23 50
8 38 25 58 52 82 70 60
10 28 15 12 34 9 8 56

Sample Output:

Max Heap
50 60 65 72 12 23 86 98
Min Heap
60 58 52 38 82 70 25 8
Not Heap
56 12 34 28 9 8 15 10

虽然是30分的题但是不难

题目大意：判断这个完全二叉树是不是堆，输出其后序

主要根据完全二叉树的性质来做，根节点为i，则两个孩子是 2*i+1，2*i+2

#include <bits/stdc++.h>
#define Max 1100
using namespace std;
int n, m, a[Max];
//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;
}
void postorder(int i) {
  if(i >= n) return ;
  postorder(2*i+1);
  postorder(2*i+2);
  if(i != 0) //为了满足输出格式的要求 
  cout << a[i] << " ";
}
int main() {

  cin >> m >> n;
  for(int j = 0; j < m; j++) {
    memset(a, 0, sizeof(a));
    for(int i = 0; i < n; i++)
      cin >> a[i];
    if(isMaxHeap(a)) {
      cout << "Max Heap" << endl;
    } else if(isMinHeap(a)) {
      cout << "Min Heap" << endl;
    } else cout << "Not Heap" << endl;
    postorder(0);
    cout << a[0] << endl; 
  }

  return 0;
}