PAT A1155 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<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

实现思路：
在1147这题的基础上进行了修改，要求从树的右边到左边输出根节点到叶结点路径的值，很简单采用递归遍历，并且用一个vector数组来保存序列值再输出即可。

AC代码：

#include <iostream>
#include <vector>
using namespace std;
const int N=1001;
int heap[N],n,m,val,cnt=0;
bool tag,isMin,isMax;
vector<int> temp;

void Print(int x) {
	if(x>m) return;
	temp.push_back(heap[x]);
	if(x*2+1>m&&x*2>m) {
		for(int i=0; i<temp.size(); i++) {
			printf("%d",temp[i]);
			if(i<temp.size()-1) printf(" ");
			else printf("\n");
		}
	}
	Print(x*2+1);
	Print(x*2);
	temp.pop_back();
}

bool judge() {
	for(int i=1; i<=m/2; i++) {
		if(isMax) {
			if(i*2<=m&&heap[i]<heap[i*2]) isMax=false;
			else if(i*2+1<=m&&heap[i]<heap[i*2+1]) isMax=false;
		} else {
			if(i*2<=m&&heap[i]>=heap[i*2]) isMin=false;
			else if(i*2+1<=m&&heap[i]>=heap[i*2+1]) isMin=false;
		}
	}
}

int main() {
	cin>>m;
	for(int i=1; i<=m; i++) {
		scanf("%d",&heap[i]);
	}
	tag=true;
	isMax=isMin=false;
	if(heap[1]>=heap[2]) {
		if(3<=m&&!heap[1]>=heap[3]) isMax=false;;
		isMax=true;
	} else {
		if(3<=m&&!heap[1]<heap[3]) isMin=false;
		isMin=true;
	}
	Print(1);
	judge();
	if(isMax) printf("Max Heap");
	else if(isMin) printf("Min Heap");
	else printf("Not Heap");
	return 0;
}