1155_Heap_Paths

1155:Heap Paths

题目

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

分析

题目虽然和堆有关系，但实际上只是一个深度搜索然后回溯就可以解决的问题。最开始的想法是在深搜的同时就判断一下是否满足条件，但是总是出一些奇怪的bug，递归的问题也不太好调试，就参照题解，先遍历出所有的路径情况，然后再单独判断是否符合条件。

代码

#include
#include

using namespace std;

int n;
vector heap; // 数组形式存储堆
vector path; // 存储路径 用于回溯

void dfs(int pos){ // 回溯
    if(pos >= n){
        return;
    }
    if (pos >= n/2){ // 在数组堆中 大于n/2一定是叶子结点 打印结果即可
        for(int i = 0; i> n;
    for(int i=0; iheap[i*2+1]) || (i*2+2 < n && heap[i] > heap[i*2+2])){
            min = false;
        }
    }
    if(min){
        printf("Min Heap");
    } else if(max){
        printf("Max Heap");
    } else{
        printf("Not Heap");
    }
    return 0;
}