1155 Heap Paths

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:

1 2	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:

1 2	8 8 38 25 58 52 82 70 60

Sample Output 2:

Sample Input 3:

1 2	8 10 28 15 12 34 9 8 56

Sample Output 1:

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

浅析

Q：打印从根节点到叶节点的路径

掌握在递归前后适用 Push 和 Pop 来维护路径的方法

Code

#include 
#include 
using namespace std;
int num,A[1010];
vector<int> v;
void traverse(int a){
    if(2*a>num&&2*a+1>num){
        if(a<=num){ //只有左节点递归过来的情况
            for (int i = 0; i < v.size();i++){
                printf("%d", v[i]);
                if(i-1)
                    printf(" ");
                else
                    printf("\n");
            }
        }
    }
    else{
        v.push_back(A[2 * a + 1]);
        traverse(2 * a + 1);
        v.pop_back();
        v.push_back(A[2 * a]);
        traverse(2 * a);
        v.pop_back();
    }
}

int main(){
    scanf("%d", &num);
    for (int i = 0; i < num;i++)
        scanf("%d", &A[i + 1]);
    v.push_back(A[1]);
    traverse(1);
    int min = 1,max = 1;
    for (int i = 2; i <= num;i++){< span>
        if(A[i/2]>A[i])
            min = 0;
        if(A[i/2]
            max = 0;
    }
    if(min==1)
        printf("Min Heap");
    else if(max==1)
        printf("Max Heap");
    else
        printf("Not Heap");
    return 0;
}