PAT A1147 Heaps (30point(s))

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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))

Your job is to tell if a given complete binary tree is a heap.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers: M (≤ 100), the number of trees to be tested; and N (1 < N ≤ 1,000), the number of keys in each tree, respectively. Then M lines follow, each 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, 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. Then in the next line print the tree's postorder traversal sequence. All the numbers are separated by a space, and there must no extra space at the beginning or the end of the line.

Sample Input:

3 8
98 72 86 60 65 12 23 50
8 38 25 58 52 82 70 60
10 28 15 12 34 9 8 56

Sample Output:

Max Heap
50 60 65 72 12 23 86 98
Min Heap
60 58 52 38 82 70 25 8
Not Heap
56 12 34 28 9 8 15 10

解答

#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<vector>
#include<set>

using namespace std;

int keysNum, caseNum;
bool maxHeap = false, minHeap = false;
vector<int> nodes, ans;

void postOrder(int id)
{
	if (id > keysNum) return;
	postOrder(id * 2);
	postOrder(id * 2 + 1);
	printf("%d%s", nodes[id], id == 1 ? "\n" : " ");
}

int main()
{
	scanf("%d %d", &caseNum, &keysNum);
	nodes.resize(keysNum + 1);
	for (int j = 0; j < caseNum; j++) {
		int ismin = 1, ismax = 1;
		for (int i = 1; i <= keysNum; i++) scanf("%d", &nodes[i]);
		for (int i = 2; i <= keysNum; i++) {
			if (nodes[i] > nodes[i / 2]) ismax = 0;
			if (nodes[i] < nodes[i / 2]) ismin = 0;
		}
		if (!ismax && !ismin) printf("Not Heap\n");
		else printf("%s Heap\n", ismax == 1 ? "Max" : "Min");
		postOrder(1);
	}
	return 0;
}