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
题意:
题目主要要求两点,第一从右到左输出从根节点到叶节点的所有路径,第二是判断是不是堆,大堆还是小堆。第一个问题利用dfs从右往左遍历,用vector记录路径,每次到达叶节点的时候进行输出。第二个问题,由于给的是层序序列,直接循环判断每个节点之间的大小关系即可。
C++:
#include"iostream"
#include"vector"
using namespace std;
vector<int> ans,node;
int n;
void dfs(int index){
if(index*2>n&&index*2+1>n){
if(index<=n){
for(int i=0;i<ans.size();i++)
printf("%s%d",i==0?"":" ",ans[i]);
printf("\n");
}
return;
}
ans.push_back(node[index*2+1]);
dfs(index*2+1);
ans.pop_back();
ans.push_back(node[index*2]);
dfs(index*2);
ans.pop_back();
}
int main(){
scanf("%d",&n);
node.resize(n+1);
for(int i=1;i<=n;i++)scanf("%d",&node[i]);
ans.push_back(node[1]);
dfs(1);
int isMax=1,isMin=1;
for(int i=2;i<=n;i++){
if(node[i/2]>node[i])isMin=0;
if(node[i/2]<node[i])isMax=0;
}
if(isMax)
printf("Max Heap\n");
else if(isMin)
printf("Min Heap\n");
else
printf("Not Heap\n");
return 0;
}