pat甲级 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 Ndistinct 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
考察堆的性质,总的来说很简单。
代码:
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define MAX 1000
#define DMAX 10000
using namespace std;
typedef long long ll;
int n;
int big,small;
int heap[MAX + ],t[MAX + ];
void print(int h) {
for(int i = ;i <= h;i ++) {
printf("%d",t[i]);
putchar(i < h ? ' ' : '\n');
}
}
void traversal(int k,int h) {
if(k > n) {
return ;
}
t[h] = heap[k];
if(k * > n) print(h);
if(h) {
if(t[h] > t[h - ]) small = ;
else if(t[h] < t[h - ]) big = ;
}
traversal(k * + ,h + );
traversal(k * ,h + );
}
int main() {
scanf("%d",&n);
for(int i = ;i <= n;i ++) {
scanf("%d",&heap[i]);
}
traversal(,);
if(big == small) puts("Not Heap");
else if(big) puts("Max Heap");
else puts("Min Heap");
}
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