1147 Heaps (30 分) 堆的判断-蒲公英云

1147 Heaps (30 分) 堆的判断

小咪咪 2021-10-30 02:28 356阅读 0赞

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：n次询问，m个结点，判断是否为大小堆，然后输出后序遍历。

#include <stdio.h>
#include <string.h>
#include <string>
#include <map>
#include <vector>
#include <queue>
#include <math.h>
#include <algorithm>
#include <iostream>
#define INF 0x3f3f3f3f
using namespace std;
int a[1005],m;
bool ismax()
{
    for(int i=0;i<m/2;i++)
    {
        if(i*2+1<m)
        {
            if(a[i]<=a[i*2+1])
            return false;
        }
        if(i*2+2<m)
        {
            if(a[i]<=a[i*2+2])
            return false;
        }
    }
    return true;
}
bool ismin()
{
    for(int i=0;i<m/2;i++)
    {
        if(i*2+1<m)
        {
            if(a[i]>=a[i*2+1])
            return false;
        }
        if(i*2+2<m)
        {
            if(a[i]>=a[i*2+2])
            return false;
        }
    }
    return true;
}
vector<int> v;
void post(int t)
{
    if(t>=m)return;
    if(t*2+1<m)
    post(t*2+1);
    if(t*2+2<m)
    post(t*2+2);
    v.push_back(t);
}
int main() 
{
    int n,i,j,k;
    scanf("%d%d",&n,&m);
    while(n--)
    {  
        for(i=0;i<m;i++)
        scanf("%d",&a[i]);
        if(ismax())
        printf("Max Heap\n");
        else if(ismin())
        printf("Min Heap\n");
        else
        printf("Not Heap\n");
        v.clear();
        post(0);
        for(i=0;i<v.size();i++)
        {
            if(i)printf(" ");
            printf("%d",a[v[i]]);
        }
        printf("\n");
    }    
}