1147 Heaps (30 分) 堆的判断

小咪咪 2021-10-30 02:28 221阅读 0赞

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][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：n次询问，m个结点，判断是否为大小堆，然后输出后序遍历。

#include <stdio.h>
    #include <string.h>
    #include <string>
    #include <map>
    #include <vector>
    #include <queue>
    #include <math.h>
    #include <algorithm>
    #include <iostream>
    #define INF 0x3f3f3f3f
    using namespace std;
    int a[1005],m;
    bool ismax()
    {
    	for(int i=0;i<m/2;i++)
    	{
    		if(i*2+1<m)
    		{
    			if(a[i]<=a[i*2+1])
    			return false;
    		}
    		if(i*2+2<m)
    		{
    			if(a[i]<=a[i*2+2])
    			return false;
    		}
    	}
    	return true;
    }
    bool ismin()
    {
    	for(int i=0;i<m/2;i++)
    	{
    		if(i*2+1<m)
    		{
    			if(a[i]>=a[i*2+1])
    			return false;
    		}
    		if(i*2+2<m)
    		{
    			if(a[i]>=a[i*2+2])
    			return false;
    		}
    	}
    	return true;
    }
    vector<int> v;
    void post(int t)
    {
    	if(t>=m)return;
    	if(t*2+1<m)
    	post(t*2+1);
    	if(t*2+2<m)
    	post(t*2+2);
    	v.push_back(t);
    }
    int main() 
    {
    	int n,i,j,k;
    	scanf("%d%d",&n,&m);
    	while(n--)
    	{  
    		for(i=0;i<m;i++)
    		scanf("%d",&a[i]);
    		if(ismax())
    		printf("Max Heap\n");
    		else if(ismin())
    		printf("Min Heap\n");
    		else
    		printf("Not Heap\n");
    		v.clear();
    		post(0);
    		for(i=0;i<v.size();i++)
    		{
    			if(i)printf(" ");
    			printf("%d",a[v[i]]);
    		}
    		printf("\n");
    	}	
    }

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