【PTA Advanced】1155 Heap Paths（C++）

目录

题目

Input Specification:

Output Specification:

Sample Input 1:

Sample Output 1:

Sample Input 2:

Sample Output 2:

Sample Input 3:

Sample Output 3:

思路

代码

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题目

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))

One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order.

Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (1<N≤1,000), the number of keys in the tree. Then the next line 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, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree.

Finally 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.

Sample Input 1:

8
98 72 86 60 65 12 23 50

Sample Output 1:

98 86 23
98 86 12
98 72 65
98 72 60 50
Max Heap

Sample Input 2:

8
8 38 25 58 52 82 70 60

Sample Output 2:

8 25 70
8 25 82
8 38 52
8 38 58 60
Min Heap

Sample Input 3:

8
10 28 15 12 34 9 8 56

Sample Output 3:

10 15 8
10 15 9
10 28 34
10 28 12 56
Not Heap

思路

难度评级：⭐️

1. path的输出

递归实现树的深度遍历，先访问右孩子，再访问左孩子即可。

2. 判断是否是堆

采用堆创建或者调整时的思路即可，从树的最后一个非叶子结点向上遍历，每次比对该节点和它孩子的大小是否符合大根堆/小根堆的规则

3. 大小根堆的判断如何只用一段代码实现

设置flag，大小根堆的flag值不同，在比对结点与其孩子大小时异或一下即可，具体代码见函数isHeap

代码

#include <iostream>
#include <vector>using namespace std;int n,heapFlag;
vector<int> nodes;void printPath(int nodeIndex,vector<int> path) {path.push_back(nodes[nodeIndex]);// 叶子结点时if(nodeIndex*2>n) {// 输出pathint flag=false;for(int node:path) {if(flag) cout<<" ";cout<<node;flag=true;}cout<<endl;return;}// 分支节点先遍历右孩子，再遍历左孩子if(nodeIndex*2+1<=n) printPath(nodeIndex*2+1,path);if(nodeIndex*2<=n) printPath(nodeIndex*2,path);
}// 判断树是否是heapFlag类型的heap
bool isHeap() {// 从最后一个非叶子结点开始向前遍历for(int i=n/2;i>=1;i--) {if(i*2<=n&&(nodes[i]>=nodes[i*2])^heapFlag) return false;if(i*2+1<=n&&(nodes[i]>=nodes[i*2+1])^heapFlag) return false;} return true;
}int main(int argc, char** argv) {cin>>n;nodes.resize(n+1);for(int i=1;i<=n;i++) {int node;cin>>node;nodes[i]=node;}// 递归的方式输出pathvector<int> path;printPath(1,path); // 初步判断可能是什么heapif(nodes[1]>=nodes[n]) heapFlag=1;// 大根堆 else heapFlag=0;// 小根堆// 判断树是否是heapFlag类型的heapif(isHeap()){if(heapFlag==1) cout<<"Max Heap";else cout<<"Min Heap";}else cout<<"Not Heap";return 0;
}