1155 Heap Paths （30 分) 判断大小顶堆

青旅半醒 2022-03-02 16:05 145阅读 0赞

1155 Heap Paths （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][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

给出一棵层次遍历的有n个结点的树，输出 从右到左的 从根结点到每个叶子结点的路径，并判断大小顶堆。

大/小顶堆：每个结点都比自己的子节点大/小。

(下标0开始)二叉树结点为x，左结点为2\*x+1，右结点为2\*x+2。

由根结点往下深搜，当搜到叶子节点（用x\*2+1>=n判断，即不存在左子树）时，直接输出，回溯的时候弹出该结点。

#include<stdio.h>
    #include<string.h>
    #include<math.h>
    #include<iostream>
    #include<string>
    #include<sstream>
    #include<algorithm>
    #include<map>
    #include<set>
    #include<queue>
    #include<stack>
    #include<vector>
    using namespace std;
    #define inf 0x3f3f3f3f
    #define LL long long
    int a[1005],n;
    vector<int> v;
    void dfs(int x)
    {
    	if(x*2+1>=n)
    	{
    		for(int i=0;i<v.size();i++)
    		printf("%d ",a[v[i]]);
    		printf("%d\n",a[x]);
    		return;
    	}
    	if(2*x+2<n)
    	{
    		v.push_back(x);
    		dfs(2*x+2);
    		v.pop_back();
    	}
    	if(2*x+1<n)
    	{
    		v.push_back(x);
    		dfs(2*x+1);
    		v.pop_back();
    	}
    }
    int main()
    {
    	int i,j,fm=0,fn=0;
    	scanf("%d",&n);
    	for(i=0;i<n;i++)
    	scanf("%d",&a[i]);
    	dfs(0);
    	for(i=0;i<n;i++)
    	{
    		if(i*2+1<n)
    		{
    			if(a[i]<a[i*2+1])
    			fm=1;
    			else 
    			fn=1;
    		}
    		if(i*2+2<n)
    		{
    			if(a[i]<a[i*2+2])
    			fm=1;
    			else 
    			fn=1;
    		}
    	}
    	if(fm&&fn)
    	printf("Not Heap\n");
    	else if(fm)
    	printf("Min Heap\n");
    	else
    	printf("Max Heap\n");
    }

[https_en.wikipedia.org_wiki_Heap_data_structure]: https://en.wikipedia.org/wiki/Heap_%28data_structure