pat 1155

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), 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:

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

题意：给定一个完全二叉树，要求从树的右边开始依次输出根结点到叶子结点的路径，并判断是不是大顶堆或者小顶堆。

思路：数组存这颗完全二叉树，以类似于中序遍历的方式递归将结点存入vector中，当到达叶子结点后输出整个vector中的元素。判断是否为堆只需要设置两个变量，加入在遍历输出的过程中发现不满足堆的需求，则改变这两个变量的值，最后如果两个变量的值有一个没被改变，则说明是相应的堆。否则不是堆

代码如下：

#include<cstdio>
#include<vector>
int node[1005];
using namespace std;
int n;
int minV=1;
int maxV=1;
void inOrder(vector<int> v,int root){
    v.push_back(root);
    if(2*root+1<=n){
        inOrder(v,2*root+1);
    }
    if(2*root<=n){
        inOrder(v,2*root);
    }
    else{
        for(vector<int>::iterator it=v.begin();it!=v.end();it++){
            if(it!=v.end()-1){
                if((it+1)!=v.end()){
                    if(node[*it]>node[*(it+1)]){
                        minV=0;
                    }
                    if(node[*it]<node[*(it+1)]){
                        maxV=0;
                    }    
                }
                printf("%d ",node[*it]);
            }
            else
                printf("%d",node[*it]);
        }
        printf("
");
    }
}
int main(){

    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d",&node[i]);
    }
    vector<int> v; 
    inOrder(v,1);
    if(maxV!=0)
        printf("Max Heap
");
    if(minV!=0)
        printf("Min Heap
");
    if(maxV==0&&minV==0){
        printf("Not Heap
");
    }
    return 0;
}