1155 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

#include<iostream>
#include<vector>
#include<cmath>
using namespace std;
int n;
vector<int> binary_tree;

vector<int> gap;

vector<int> output_tree;

int flag_cout_neg, flag_cout_pos;
void out_put_tree(int start){

    int z = start;
    output_tree.clear();
    while (z > 0)
    {
        output_tree.push_back(binary_tree[z]);
        // cout << binary_tree[z] << "====" << z << endl;cout << binary_tree[z] << "====" << z << endl;
        z = z / 2;
       
    }
    printf("%d", output_tree.back());
    int min_or_max = output_tree.back();
    int neg_cnt = 0, pos_cnt = 0, zero = 0;;
    for(int j = output_tree.size() - 2; j >= 0; j--){
        
        if(min_or_max - output_tree[j] > 0){

            pos_cnt++;

        }else if(min_or_max - output_tree[j] < 0)
        {
            neg_cnt++;

        }else if(min_or_max - output_tree[j] == 0)
        {
            zero++;
        }
        
        

        printf(" %d", output_tree[j]);
        min_or_max = output_tree[j];
    }
    cout << endl;
    if(pos_cnt == 0 && neg_cnt != 0)

        flag_cout_neg++;

    if(pos_cnt != 0 && neg_cnt == 0)

        flag_cout_pos++;

}

int main(){
    flag_cout_neg = 0;
    flag_cout_pos = 0;
    int child_start, child_end, child_right_1, child_right_2, hight;
    
    cin >> n;
    binary_tree.push_back(0);
    for(int i = 1; i <= n; i++){

        int temp;

        scanf("%d", &temp);

        binary_tree.push_back(temp);


    }


    // for(int i = 0; i < binary_tree.size(); i ++){

    //     cout << binary_tree[i] << endl;
    // }

    hight = log(n) / log(2) + 1;
    child_start = n / 2 + 1;
    child_end = n;
    child_right_1 = pow(2, hight - 1) - 1;
    child_right_2 = pow(2, hight) - 1;

    // cout << hight << endl;
    // cout << child_start << endl;
    // cout << child_end << endl;
    // cout << child_right_1 << endl;
    // cout << child_right_2 << endl;
    if(child_end == child_right_2){

        for(int i = child_end; i >= child_start; i--){
            
            
            out_put_tree(i);

            // cout << "1";
        }

    }else
    {   
        
        
        for(int i = child_right_1; i >= child_start; i--){

            out_put_tree(i);
            // cout << "2";
        }
        


        for(int i = child_end; i > child_right_1; i--){

            out_put_tree(i);
            // cout << "3";
        }


        
    }
    
    if(flag_cout_pos == child_end - child_start + 1){

        cout << "Max Heap" << endl;

    }else if(flag_cout_neg == child_end - child_start + 1)
    {
        cout << "Min Heap" << endl;
    }else
    {
        cout << "Not Heap" << endl;
    }
    
    


    return 0;
}