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

题意：
给定层序遍历的树，判断是否为大小堆。

思路：
现将输出转化为一棵树，这样就好做了，就是比较暴力
看看 柳婼 の blog 是怎么做的
题解：

#include<cstdlib>
#include<cstdio>
#include<vector>
using namespace std;
struct node {
    int value;
    int left;
    int right;
};
bool isMaxHeap(vector<node> nodes, int now) {
    bool isMax = true;
    if (now * 2 < nodes.size()) {
        if (nodes[now].value < nodes[now * 2].value) {
            isMax = false;
        }
        else {
            if (!isMaxHeap(nodes, now * 2)) {
                isMax = false;
            }
        }
    }
    if (now * 2 + 1 < nodes.size()) {
        if (nodes[now].value < nodes[now * 2 + 1].value) {
            isMax = false;
        }
        else {
            if (!isMaxHeap(nodes, now * 2 + 1)) {
                isMax = false;
            }
        }
    }
    return isMax;
}
bool isMinHeap(vector<node> nodes, int now) {
    bool isMin = true;
    if (now * 2 < nodes.size()) {
        if (nodes[now].value > nodes[now * 2].value) {
            isMin = false;
        }
        else {
            if (!isMinHeap(nodes, now * 2)) {
                isMin = false;
            }
        }
    }
    if (now * 2 + 1 < nodes.size()) {
        if (nodes[now].value > nodes[now * 2 + 1].value) {
            isMin = false;
        }
        else {
            if (!isMinHeap(nodes, now * 2 + 1)) {
                isMin = false;
            }
        }
    }
    return isMin;
}
void PostOrder(vector<node> nodes, int now) {
    if (now * 2 < nodes.size()) {
        PostOrder(nodes, now * 2);
    }
    if (now * 2 + 1 < nodes.size()) {
        PostOrder(nodes, now * 2 + 1);
    }
    //nodes[nodes.size() - 1]这个结点不一定是先输出的。
    printf("%d%s", nodes[now].value, now == 1 ? "\n" : " ");
}
int main() {
    int n, m;
    scanf("%d %d", &n, &m);
    for (int i = 0; i < n; i++) {
        vector<node> nodes(m+1);
        for (int j = 1; j <= m; j++) {
            scanf("%d", &nodes[j].value);
            nodes[j].left = j * 2;
            nodes[j].right = j * 2 + 1;
        }
        if (isMaxHeap(nodes, 1)) {
            printf("Max Heap\n");
        }
        else if(isMinHeap(nodes, 1)) {
            printf("Min Heap\n");
        }
        else {
            printf("Not Heap\n");
        }
        PostOrder(nodes, 1);
    }
    return 0;
}