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

AC代码：

#include<bits/stdc++.h>
using namespace std;
const int maxn=10010;
#define inf 0x3fffffff
int heap[maxn];
int n,m,judge;
bool minH(){
    for(int i=1;i<=m;i++){
        if(i*2>m){
            break;
        }
        if(heap[i*2]<heap[i]){
            return false;
        }
        if(i*2+1>m){
            break;
        }
        if(heap[i*2+1]<heap[i]){
            return false;
        }
    }
    return true;
}
bool maxH(){
    for(int i=1;i<=m;i++){
        if(i*2>m){
            break;
        }
        if(heap[i*2]>heap[i]){
            return false;
        }
        if(i*2+1>m){
            break;
        }
        if(heap[i*2+1]>heap[i]){
            return false;
        }
    }
    return true;
}
void post_order(int v){
    if(v>m){
        return;
    }
    if(v*2<=m){
        post_order(v*2);
    }
    if(v*2+1<=m){
        post_order(v*2+1);
    }
    if(judge==1){
          printf("%d\n",heap[v]);
    }
    else{
        judge--;
        printf("%d ",heap[v]);
    }
    
}
int main(){
    scanf("%d %d",&n,&m);
    for(int i=0;i<n;i++){
        fill(heap,heap+maxn,0);
        for(int j=1;j<=m;j++){
            scanf("%d",&heap[j]);
        }
        if(minH()){
            printf("Min Heap\n");
        }
        else if(maxH()){
            printf("Max Heap\n");
        }
        else{
            printf("Not Heap\n");
        }
        judge=m;
        post_order(1);
    }
    return 0;
}