[PAT] 1147 Heaps（30 分）

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

题意：
给定层序遍历的树，判断是否为大小堆。

思路：
先将输出转化为一棵树，这样就好做了，就是比较暴力
看看 柳婼 の blog 是怎么做的
题解：

 #include<cstdlib>
 #include<cstdio>
 #include<vector>
 using namespace std;
 struct node {
     int value;
     int left;
     int right;
 };
 bool isMaxHeap(vector<node> nodes, int now) {
     bool isMax = true;
      < nodes.size()) {
         ].value) {
             isMax = false;
         }
         else {
             )) {
                 isMax = false;
             }
         }
     }
      +  < nodes.size()) {
          + ].value) {
             isMax = false;
         }
         else {
              + )) {
                 isMax = false;
             }
         }
     }
     return isMax;
 }
 bool isMinHeap(vector<node> nodes, int now) {
     bool isMin = true;
      < nodes.size()) {
         ].value) {
             isMin = false;
         }
         else {
             )) {
                 isMin = false;
             }
         }
     }
      +  < nodes.size()) {
          + ].value) {
             isMin = false;
         }
         else {
              + )) {
                 isMin = false;
             }
         }
     }
     return isMin;
 }
 void PostOrder(vector<node> nodes, int now) {
      < nodes.size()) {
         PostOrder(nodes, now * );
     }
      +  < nodes.size()) {
         PostOrder(nodes, now *  + );
     }
     //nodes[nodes.size() - 1]这个结点不一定是先输出的。
     printf( ? "\n" : " ");
 }
 int main() {
     int n, m;
     scanf("%d %d", &n, &m);
     ; i < n; i++) {
         vector<node> nodes(m+);
         ; j <= m; j++) {
             scanf("%d", &nodes[j].value);
             nodes[j].left = j * ;
             nodes[j].right = j *  + ;
         }
         )) {
             printf("Max Heap\n");
         }
         )) {
             printf("Min Heap\n");
         }
         else {
             printf("Not Heap\n");
         }
         PostOrder(nodes, );
     }
     ;
 }