PAT A1155 2019.08.14 【深度回溯 完全二叉树建树】

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))

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

思路分析：

利用完全二叉树性质建树。

DFS+stack求根到叶子路径。

利用上一步得到的路径，判断堆的类型。

#include<cstdio>
#include<iostream>
#define MAX 2000
using namespace std;

typedef struct NODE{
	int data;
	struct NODE *left;
	struct NODE *right;
}NODE;

NODE *node[MAX];
int key[MAX];
int n;
int flag1=0,flag2=0;//1-max;2-min;3-no;

void init()
{
	for(int i=0;i<MAX;i++)
	{
		node[i]=new NODE;
		node[i]->data=-1;
		node[i]->left=NULL;
		node[i]->right=NULL;
		key[i]= -1;
	}
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&key[i]);
	}
	
	for(int i=1;i<=n;i++)
	{
		node[i]->data=key[i];
		if(key[2*i]!=-1)node[i]->left=node[2*i];
		if(key[2*i+1]!=-1)node[i]->right=node[2*i+1];
	}
}


void preorder(NODE *root)
{
	if(root==NULL)return;
	printf("%d ",root->data);
	preorder(root->left);
	preorder(root->right);
}

NODE *stack[MAX];int top=-1;
void dfs(NODE *root)
{
	if(root->left!=NULL||root->right!=NULL)//不是叶子结点 
	{
//		printf("%d ",root->data);
        stack[++top]=root;
		if(stack[top]->right!=NULL)dfs(stack[top]->right);
		if(stack[top]->left!=NULL)dfs(stack[top]->left);
		top--;
		return; 
	}
	else//是叶子结点 
	{
		stack[++top]=root;
        for(int i=0;i<top;i++)printf("%d ",stack[i]->data);
        printf("%d\n",stack[top]->data);
        
        for(int i=1;i<=top;i++)
        {
        	if(stack[i]->data>stack[i-1]->data)flag2=1;
        	if(stack[i]->data<stack[i-1]->data)flag1=1;
		}
        top--;
		return;
	}
	
}

int main()
{
	init();
	NODE *root = node[1];
//	preorder(root);
	dfs(root);
		if(flag1==1&&flag2==1)printf("Not Heap");
	    if(flag1==1&&flag2==0)printf("Max Heap");
	    if(flag1==0&&flag2==1)printf("Min Heap");
}