PAT甲级2018冬季7-4 1155 Heap Paths(30 分)
算法笔记总目录
关键英语单词解释
1155 Heap Paths(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))
One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order.
Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not.
Input Specification:
Each input file contains one test case. For each case, the first line gives a positive integer N (1<N≤1,000), the number of keys in the tree. Then the next line 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, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree.
Finally 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.
Sample Input 1:
8
98 72 86 60 65 12 23 50
Sample Output 1:
98 86 23
98 86 12
98 72 65
98 72 60 50
Max Heap
Sample Input 2:
8
8 38 25 58 52 82 70 60
Sample Output 2:
8 25 70
8 25 82
8 38 52
8 38 58 60
Min Heap
Sample Input 3:
8
10 28 15 12 34 9 8 56
Sample Output 3:
10 15 8
10 15 9
10 28 34
10 28 12 56
Not Heap
代码一来自柳诺
题目大意:给出一颗完全二叉树,打印出从根节点到所有叶节点的路径,打印顺序先右后左,即先序遍历的镜像。然后判断该树是大顶堆、小顶堆或者不是堆~
分析:1.深搜打印出所有路径(从右往左,即先序的镜像),vector保存一路上的节点,通过push和pop回溯,维护路径,index <= n是对只有左叶节点没有右叶节点的点特判
2.判断是否为堆:从第二个节点开始遍历,如果比父节点小,就不是小顶堆,如果比父节点大,就不是大顶堆~
#include <iostream>
#include <vector>
using namespace std;
vector<int> v;
int a[1009], n, isMin = 1, isMax = 1;
void dfs(int index) {
if (index * 2 > n && index * 2 + 1 > n) {
if (index <= n) {
for (int i = 0; i < v.size(); i++)
printf("%d%s", v[i], i != v.size() - 1 ? " " : "\n");
}
} else {
v.push_back(a[index * 2 + 1]);
dfs(index * 2 + 1);
v.pop_back();
v.push_back(a[index * 2]);
dfs(index * 2);
v.pop_back();
}
}
int main() {
cin >> n;
for (int i = 1; i <= n; i++)
scanf("%d", &a[i]);
v.push_back(a[1]);
dfs(1);
for (int i = 2; i <= n; i++) {
if (a[i/2] > a[i]) isMin = 0;
if (a[i/2] < a[i]) isMax = 0;
}
if (isMin == 1)
printf("Min Heap");
else
printf("%s", isMax == 1 ? "Max Heap" : "Not Heap");
return 0;
}
代码二
完全层序建树(练习使用,考试第一种方法即可)
#include<bits/stdc++.h>
using namespace std;
struct node{
int val;
node *lchild,*rchild;
};
int n,level[1010],x=0,a[1010],isMin = 1, isMax = 1;
node *create(int x,node *root)//1号位开始
{
if(x>n) return NULL;
root->val=level[x];
root->lchild=create(x*2,new node);
root->rchild=create(x*2+1,new node);
return root;
}
void printTree(node *root){
if(root->rchild== NULL && root->lchild== NULL){
printf("%d",a[0]);
for(int i=1;i<x;i++) printf(" %d",a[i]);
printf(" %d\n",root->val);
return;
}
a[x]=root->val;
x++;
if(root->rchild != NULL)printTree(root->rchild);
if(root->lchild != NULL)printTree(root->lchild);
x--;
}
int main(){
scanf("%d",&n);
node *root = new node;
for (int i = 1; i <= n; i++)
scanf("%d", &level[i]);
printTree(create(1,root));
for (int i = 2; i <= n; i++) {
if (level[i/2] > level[i]) isMin = 0;
if (level[i/2] < level[i]) isMax = 0;
}
if (isMin == 1)
printf("Min Heap");
else
printf("%s", isMax == 1 ? "Max Heap" : "Not Heap");
return 0;
}
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