1147 Heaps （30 分）（层序转后序，堆，树的遍历）

最新推荐文章于 2025-02-09 09:00:00 发布

小火汁猛猛

最新推荐文章于 2025-02-09 09:00:00 发布

阅读量171

点赞数 1

分类专栏： c++ 甲级文章标签： PAT

本文链接：https://blog.youkuaiyun.com/qq_42068614/article/details/87940245

版权

c++ 同时被 2 个专栏收录

115 篇文章

订阅专栏

甲级

92 篇文章

订阅专栏

本文介绍了一种算法，用于判断给定的完全二叉树是否满足最大堆或最小堆的性质，并通过示例展示了如何使用级序遍历和后序遍历来识别和打印堆类型。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

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 <algorithm>
#include <cmath>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <string>
#include <cctype>
#include <string.h>
#include <cstdio>
#include <unordered_set>
using namespace std;
int m,n;
vector<int> level,post;
void postOrder(int index){
    if(index>=n) return;
    postOrder(index*2+1);
    postOrder(index*2+2);
    printf("%d%s",level[index],index==0?"\n":" ");
}
int main() {
    cin>>m>>n;
    level.resize(n);
    post.resize(n);
    for(int i=0;i<m;i++){
        for(int j=0;j<n;j++)
            cin>>level[j];
        int flag=level[0]>level[1]?1:-1;
        for(int j=0;j<=(n-1)/2;j++){
            int left=j*2+1,right=j*2+2;
            if(flag==1&&(level[left]>level[j]||(right<n&&level[right]>level[j]))) flag=0;
            if(flag==-1&&(level[left]<level[j]||(right<n&&level[right]<level[j]))) flag=0;
        }
        if(flag==0) printf("Not Heap\n");
        else printf("%s Heap\n",flag==1?"Max":"Min");
        postOrder(0);
    }
    return 0;
}