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:

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


这道题题意：已知一个树，求根节点到叶子节点的每条路径遍历，并且判断是大根堆，小跟堆，还是不是堆

#include <iostream>
#include <vector>
int N, arr[1100];
int isHeap;
using namespace std;
void dfs(int root, vector<int> path) {
    path.push_back(arr[root]);
    if(2 * root + 2 < N) {
        if(isHeap == 1 && arr[root] < arr[2 * root + 2]) isHeap = -1; 
        if(isHeap == 0 && arr[root] > arr[2 * root + 2]) isHeap = -1; 
        dfs(2 * root + 2, path);
    }
    if(2 * root + 1 < N) {
        if(isHeap == 1 && arr[root] < arr[2 * root + 1]) isHeap = -1; 
        if(isHeap == 0 && arr[root] > arr[2 * root + 1]) isHeap = -1; 
        dfs(2 * root + 1, path);
    }
    if(2 * root + 1 >= N && 2 * root + 2 >= N) {
        if(path.size() != 0) printf("%d", path[0]);
        for(int i = 1; i < path.size(); i++)
            printf(" %d", path[i]);
        putchar('
');
    }
}
int main() {
    scanf("%d", &N);
    for(int i = 0; i < N; i++)
        scanf("%d", &arr[i]);
    isHeap = arr[0] > arr[1]; 
    vector<int> path;
    dfs(0, path);
    // 0节点是否比1节点大， 大跟堆 1， 小跟堆 0， 不是堆 -1
    if(isHeap == 1) printf("Max Heap
");
    else if(isHeap == 0) printf("Min Heap
");
    else printf("Not Heap
");
    return 0;
}