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
题目大意: 以完全二叉树层次遍历的顺序输入结点key,按从根到叶子输出结点值并按总右子树到左子树的顺序,最后判断是大根堆还是小根堆或者不是堆。
思路:
将这些结点按顺序存储,构建的时候查找完全二叉树寻找孩子结点可用,左2x,右2x+1主要用到深度优先遍历注意:
深搜有一个回退过程,要记住模板代码:(C++)
#include<iostream> #include<vector> using namespace std; int a[1009] = {0}; int n, isMax=1, isMin=1; vector<int> v; void dfs(int index) { if(index*2>n && index*2+1>n) //无左右子树的结点,为叶子结点 { if(index<=n) //这个主要用于判断这个结点是否是树的叶子结点 { for(int i=0; i<v.size(); i++) { //这个打印方便 printf("%d%s", v[i], i != v.size()-1? " ": "\n"); } } } else { v.push_back(a[index*2+1]); //记录右节点 dfs(index*2+1);//对右子树进行遍历 v.pop_back(); //遍历完了之后弹出刚刚放进去的结点 v.push_back(a[index*2]); //左节点 dfs(index*2); v.pop_back(); } } int main() { cin>>n; for(int i=1; i<=n; i++) scanf("%d",&a[i]); v.push_back(a[1]); //根结点每条路径里面都有 dfs(1); for(int i=2; i<=n; i++) { //对于每个结点都可以比较它与父节点的大小关系 if(a[i/2] > a[i]) isMin = 0; if(a[i/2] < a[i]) isMax = 0; } if(isMin == 1) printf("Min Heap"); else printf("%s", isMax == 1 ? "Max Heap" : "Not Heap"); //一行里面输出,减少代码量 return 0; }参考: https://blog.csdn.net/liuchuo/article/details/84973009