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

 

 

依然是堆的性质，再加一个后序遍历，这题30分有点多

 

#include <bits/stdc++.h>

using namespace std;
int an[1005];
int n,m;
vector<int> v;

void predfs(int x){
    if(x*2 <= m)
        predfs(x*2);
    if(x*2+1 <= m)
        predfs(x*2+1);
    v.push_back(an[x]);
}

int main(){
    cin >> n >> m;
    while(n--){
        v.clear();
        bool isbig = true, islittle = true;
        for(int i = 1 ; i <= m ; ++i){
            cin >> an[i];
            if(i > 2){
                if(an[i/2] < an[i]) isbig = false;
                if(an[i/2] > an[i]) islittle = false;
            }
        }
        if(isbig)
            puts("Max Heap");
        else if(islittle)
            puts("Min Heap");
        else
            puts("Not Heap");
        predfs(1);
        for(int i = 0 ; i < v.size(); ++i)
            printf("%d%c",v[i], i == v.size()-1? '
':' ');
    }

    return 0;
}