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