1147 Heaps (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))
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
题目大意:
给出一个完全二叉树,判断是否为最大堆或者最小堆,或者既不是最大堆也不是最小堆。然后后序遍历输出
思路:
1、设置两个指示位,ismax=1.ismin=1,如果父节点比任意一个子节点大,则不是最小堆,如果父节点比任意一个子节点小,则不是最大堆。
2、后序遍历的非递归实现就是设置标志位,第三次访问的时候输出。
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.StreamTokenizer;
import java.util.Stack;
public class Main {
static int M, N;
static int[] heap;
static int flag = 1;
public static void main(String[] args) throws IOException {
// TODO Auto-generated method stub
StreamTokenizer in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
in.nextToken();
M = (int) in.nval;
in.nextToken();
N = (int) in.nval;
for (int i = 0; i < M; i++) {
heap = new int[N + 1];
for (int j = 1; j < N + 1; j++) {
in.nextToken();
heap[j] = (int) in.nval;
}
int ismax = 1, ismin = 1;
for (int j = 1; j < N + 1; j++) {
if (2 * j < N + 1) {
int child = 2 * j;
if (child + 1 < N + 1 && heap[child] > heap[child + 1])
child++;
if (heap[j] > heap[child])
ismin = 0;
child = 2 * j;
if (child + 1 < N + 1 && heap[child] < heap[child + 1])
child++;
if (heap[j] < heap[child])
ismax = 0;
} else
break;
}
if (ismax == 1)
System.out.println("Max Heap");
else if (ismin == 1)
System.out.println("Min Heap");
else
System.out.println("Not Heap");
// postOrder(1);
post2();
flag = 1;
System.out.println();
}
}
private static void post2() {
// TODO Auto-generated method stub
Stack<Integer> st = new Stack<>();
int root = 1;
int[] visit = new int[N + 1];
while (root >= 1 && root < N + 1 || !st.isEmpty()) {
while (root >= 1 && root < N + 1) {
st.push(root);
visit[root] = 1;
root = root * 2;
}
if (!st.isEmpty()) {
int num = st.peek();
if (visit[num] == 1) {
root = 2 * num + 1;
visit[num] =2;
} else if (visit[num] == 2) {
int tmp = st.pop();
if (flag == 1) {
System.out.print(heap[tmp]);
flag = 0;
} else
System.out.print(" " + heap[tmp]);
root = N + 1;
}
}
}
}
private static void postOrder(int root) {
// TODO Auto-generated method stub
if (2 * root < N + 1)
postOrder(2 * root);
if (2 * root + 1 < N + 1)
postOrder(2 * root + 1);
if (flag == 1) {
System.out.print(heap[root]);
flag = 0;
} else
System.out.print(" " + heap[root]);
}
}