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
AC代码:
#include<bits/stdc++.h> using namespace std; const int maxn=10010; #define inf 0x3fffffff int n; int heap[maxn]; vector<int> v; bool maxH(){ for(int i=1;i<=n;i++){ if(i*2>n){ break; } if(heap[i*2]>heap[i]){ return false; } if(i*2+1>n){ break; } if(heap[i*2+1]>heap[i]){ return false; } } return true; } bool minH(){ for(int i=1;i<=n;i++){ if(i*2>n){ break; } if(heap[i*2]<heap[i]){ return false; } if(i*2+1>n){ break; } if(heap[i*2+1]<heap[i]){ return false; } } return true; } vector<int> path,tempath; void dfs(int u){ if(u*2>n){ v.push_back(heap[u]); for(auto it=v.begin();it!=v.end();it++){ printf("%d",*it); if(it!=v.end()-1){ printf(" "); } } printf("\n"); v.pop_back(); return ; } v.push_back(heap[u]); if(u*2+1<=n){ dfs(u*2+1); } if(u*2<=n){ dfs(u*2); } v.pop_back(); } int main(){ scanf("%d",&n); heap[0]=0; for(int i=1;i<=n;i++){ scanf("%d",&heap[i]); } dfs(1); if(maxH()){ printf("Max Heap\n"); } else if(minH()){ printf("Min Heap\n"); } else{ printf("Not Heap\n"); } return 0; }