PAT 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

 

#include<iostream>
#include<vector>
#include<algorithm>
#include<stack>
using namespace std;
int n, m;
bool isHeap1(vector<int>& v){//判断大堆顶
  int j = n/2;
  while(j>0){
    if(v[j]>=v[j*2]){
      if(j*2+1<=n && v[j]>=v[j*2+1] || j*2+1>n) j--;
      else return false;
    }
    else return false;
  }
  return true;
}

bool isHeap2(vector<int>& v){//判断小堆顶
  int j=n/2;
  while(j>0){
    if(v[j]<=v[j*2]){
      if(j*2+1<=n && v[j]<=v[j*2+1] || j*2+1>n) j--;
      else return false;
    }
    else return false;
  }
  return true;
}
vector<int>  vis(1001, false), v(1001);
void postOrder(){//非递归后序遍历
    stack<int> s;
    vector<int> post;
    int idx;
    s.push(1);
    while(s.size()){
        idx = s.top();
        if(idx*2<=n && !vis[idx*2]){
            s.push(idx*2);
            vis[idx*2] = true;
        }else{
            post.push_back(v[s.top()]);
            s.pop();
            if(s.size()){
            idx = s.top()*2+1;
            if(idx<=n && !vis[idx]){
                s.push(idx);
                vis[idx] = true;
            }
            }
        }
    }
    for(int i=0; i<post.size(); i++){
        if(i==0) printf("%d", post[i]);
        else printf(" %d", post[i]);
    }
    printf("
");
}
int main(){
  int i, j;
  scanf("%d %d", &m, &n);
  for(i=0; i<m; i++){
    for(j=1; j<=n; j++)scanf("%d", &v[j]);
    bool flag;
      fill(vis.begin(), vis.end(), false);
    if(v[1]>=v[2] && v[1]>=v[3]){
      flag = isHeap1(v);
        if(flag) printf("Max Heap
"); 
        else printf("Not Heap
"); 
        postOrder();
    }else {
      flag = isHeap2(v);
        if(flag) printf("Min Heap
"); 
        else printf("Not Heap
"); 
        postOrder();
    }
  }
  return 0;
}