PAT 1110 Complete Binary Tree

本文介绍了一种通过输入节点关系来判断一棵树是否为完全二叉树的算法,并提供了完整的C++实现代码。该算法首先读取每个节点的左右子节点信息,然后使用深度优先搜索遍历树结构,判断其是否符合完全二叉树的定义。

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1110. Complete Binary Tree (25)

Given a tree, you are supposed to tell if it is a complete binary tree.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (<=20) which is the total number of nodes in the tree -- and hence the nodes are numbered from 0 to N-1. Then N lines follow, each corresponds to a node, and gives the indices of the left and right children of the node. If the child does not exist, a "-" will be put at the position. Any pair of children are separated by a space.

Output Specification:

For each case, print in one line "YES" and the index of the last node if the tree is a complete binary tree, or "NO" and the index of the root if not. There must be exactly one space separating the word and the number.

Sample Input 1:
9
7 8
- -
- -
- -
0 1
2 3
4 5
- -
- -
Sample Output 1:
YES 8
Sample Input 2:
8
- -
4 5
0 6
- -
2 3
- 7
- -
- -
Sample Output 2:
NO 1
#include <cstdio>
#include <cstring>
#include <queue>
#include <iostream>
using namespace std;
int tree[25][2];
int n,fa;
void dfs(){
	int last=fa,count=1;
	queue<int> q;
	q.push(fa);
	while(!q.empty()){
		int t=q.front();
		q.pop();
		if(tree[t][0]!=-1){
			q.push(tree[t][0]);
			last=tree[t][0];
			count++;
		}
		else{
			break;
		}
		if(tree[t][1]!=-1){
			q.push(tree[t][1]);
			last=tree[t][1];
			count++;
		}
		else{
			break;
		}
	}
	if(count==n){
		cout<<"YES "<<last<<endl;
	}
	else{
		cout<<"NO "<<fa<<endl;
	}
}
int Get(){
	char s[5];
	scanf("%s",s);
	if(s[0]=='-'){
		return -1;
	}
	if(s[1]){
		return (s[0]-'0')*10+s[1]-'0';
	}
	else{
		return s[0]-'0';
	}
}
int main(){
	char ch[3];
	int book[25];
	memset(book,0,sizeof(book));
	cin>>n;
	for(int i=0;i<n;i++){
		tree[i][0]=Get();
		if(tree[i][0]!=-1)
			book[tree[i][0]]=1;
		tree[i][1]=Get();
		if(tree[i][1]!=-1)
			book[tree[i][1]]=1;
	}
	for(int i=0;i<n;i++){
		if(!book[i]){
			fa=i;
			break;
		}
	}
	dfs();
	return 0;
}


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