Problem #
Source: [PAT ]
Description #
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 56Sample 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 10Solution #
Code #
#include <iostream>
#include <algorithm>
#define MAX_M 1002
#define MAX_N 102
using namespace std;
struct Node
{
int val;
Node *lch, *rch;
Node()
{
lch = NULL;
rch = NULL;
}
};
int n, m, out_index;
int list[MAX_M];
Node *create(int v)
{
Node *root = new Node;
root->val = list[v];
if ((2 * v) <= m)
{
root->lch = create(2 * v);
}
else
{
return root;
}
if ((2 * v + 1) <= m)
{
root->rch = create(2 * v + 1);
return root;
}
return root;
}
void postOrder(Node *root)
{
if(root == NULL){
return;
}
postOrder(root->lch);
postOrder(root->rch);
if (out_index != 0)
{
cout << " ";
}
cout << root->val;
out_index++;
}
bool checkBigHeap(Node *root)
{
int a, b;
if (root->lch == NULL)
{
return true;
}
if (root->rch == NULL)
{
if (root->lch->val > root->val)
{
return false;
}
else
{
return true;
}
}
a = root->lch->val;
b = root->rch->val;
a = max(a, b);
if (a > root->val)
{
return false;
}
else
{
return checkBigHeap(root->lch) && checkBigHeap(root->rch);
}
}
bool checkSmallHeap(Node *root)
{
int a, b;
if (root->lch == NULL)
{
return true;
}
if (root->rch == NULL)
{
if (root->lch->val< root->val)
{
return false;
}
else
{
return true;
}
}
a = root->lch->val;
b = root->rch->val;
a = min(a, b);
if (a < root->val)
{
return false;
}
else
{
return checkSmallHeap(root->lch) && checkSmallHeap(root->rch);
}
}
int checkBigORSmall(Node *root)
{
bool temp = true;
temp = checkBigHeap(root);
if (temp)
{
cout << "Max Heap" << endl;
return 1;
}
temp = checkSmallHeap(root);
if (temp)
{
cout << "Min Heap" << endl;
return 2;
}
cout << "Not Heap" << endl;
return 3;
}
int main()
{
int i, j, t;
Node *root;
while (cin >> n >> m)
{
for (i = 0; i < n; i++) //n行
{
for (j = 1; j <= m; j++) //m个
{
cin >> t;
list[j] = t;
}
root = create(1);
out_index = 0;
t = checkBigORSmall(root);
postOrder(root);
cout << endl;
delete root;
}
}
return 0;
}
