pat 1147

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

题意：给定一个完全二叉树，要求判断是否是堆，并输出这个完全二叉树的后序遍历序列

思路：数组存放完全二叉树，判断堆只需一次检查每个元素是否满足堆的条件。后序遍历序列参考树的四种遍历方法（递归实现）

代码如下：

#include<cstdio>
#include<vector>
using namespace std;
vector<int> v;
void check(){
    int max=1;
    int min=1;
    for(int i=1;i<=v.size();i++){
        if(max==0&&min==0){
            printf("Not Heap
");
            return; 
        } 
        if(2*i<v.size()){
            if(v[i]>=v[i*2])
                min=0;
            if(v[i]<=v[i*2])
                max=0;
        }
        if(2*i+1<v.size()){
            if(v[i]>=v[i*2+1])
                min=0;
            if(v[i]<=v[i*2+1])
                max=0;
        }
    }
    if(max==1)
        printf("Max Heap
");
    if(min==1)
        printf("Min Heap
");
}
void postOrder(int i){
    if(i<v.size()){
        if(2*i<v.size())
            postOrder(2*i);
        if(2*i+1<v.size())
            postOrder(2*i+1);
        if(i==1)
            printf("%d",v[i]);
        else
            printf("%d ",v[i]);
    }
}
int main(){
    int n,m;
    scanf("%d%d",&n,&m);
    v.resize(m+1);
    for(int i=0;i<n;i++){
        v.clear();
        v.resize(m+1);
        for(int j=1;j<=m;j++){
            scanf("%d",&v[j]);
        }
        check();
        postOrder(1);
        printf("
");
    }
    return 0;
}