PAT-A 真题 – 1147 Heaps

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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

题目大意:给定完全二叉树的层序遍历序列,判断这个二叉树是大顶堆还是小顶堆还是根本就不是堆。

再输出二叉树的后序遍历序列。

判断是不是堆,只需要判断每一个节点的左右孩子即可,特别注意小心叶子节点或没有右孩子的节点发送越界。

代码:

#include <iostream>
using namespace std;
#define MAXN 1010
//判断堆的类型 
void Judge(int H[], int qcnt){
  if(H[1] > H[2]){  //只能是大顶堆或非堆 
    for(int i = 1; i <= qcnt; i++){
      int lchild = 2 * i, rchild = 2 * i + 1;
      if(  (lchild <= qcnt && H[lchild] > H[i])  || \
        (rchild <= qcnt && H[rchild] > H[i])
      ) {
        cout << "Not Heap";
        return;
      }
    }
    cout << "Max Heap";
  }else{        //只能是小顶堆或非堆 
    for(int i = 1; i <= qcnt; i++){
      int lchild = 2 * i, rchild = 2 * i + 1;
      if(  (lchild <= qcnt && H[lchild] < H[i])  || \
        (rchild <= qcnt && H[rchild] < H[i])
      ) {
        cout << "Not Heap";
        return;
      }
    }
    cout << "Min Heap";
  }
}
//静态二叉树的递归后序遍历 
void PostOrder(int root, int H[], int qcnt, bool space){
  if(root > qcnt) return;    //叶子节点,直接ban 
  int lchild = 2 * root, rchild = 2 * root + 1;  //定义左孩子和有孩子
  PostOrder(lchild, H, qcnt, true);
  PostOrder(rchild, H, qcnt, true);
  cout << H[root];
  if(space) cout << ' ';  //是否输出空格 
}

int main(){
  int icnt, qcnt;
  cin >> icnt >> qcnt;
  while(icnt--){
    //定义静态树 
    int H[MAXN];
    //读入层序序列 
    for(int i = 1; i <= qcnt; i++)
      cin >> H[i];
    //执行判断 
    Judge(H, qcnt);
    cout << endl;
    //执行后序遍历 
    PostOrder(1, H, qcnt, false);
    cout << endl;
  }
  
  return 0;
}

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