1155 Heap Paths (30 分)

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), 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


首先涉及了一些堆的思想，但是用来用去还是当成树来用。
二叉树都已经写好了，然后从最右边的节点路径输出来。

#include <bits/stdc++.h>
using namespace std;
int n;
int an[2005];
bool isbig = true, islittle = true;
vector<int> v;
void dfs(int x){
    if(x*2 > n && x*2+1 > n){
        for(int i = 0; i < v.size(); i++){
            printf("%d%c", v[i], i == v.size()-1?'\n':' ');
        }
    }else{
        if(x*2+1 <= n){
            v.push_back(an[x*2+1]);
            dfs(x*2+1);
            v.pop_back();
        }
        if(x*2 <= n){
            v.push_back(an[x*2]);
            dfs(x*2);
            v.pop_back();
        }
    }
}

int main(){
    cin >> n;
    for(int i = 1 ; i <= n ; ++i){
        cin >> an[i];
        if(i >= 2){
            if(an[i/2] < an[i]) isbig = false;
            if(an[i/2] > an[i]) islittle = false;
        }
    }
    v.push_back(an[1]);
    dfs(1);
    if(isbig){
        puts("Max Heap");
    }else if(islittle){
        puts("Min Heap");
    }else{
        puts("Not Heap");
    }
    return 0;
}