PAT-A1110. 二叉樹-完全二叉樹的判斷

題目鏈接：https://www.patest.cn/contests/pat-a-practise/1110
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

完全二叉樹判斷思路：層序遍歷，一個完全二叉樹中，當遍歷到某個結點沒有子結點時，那麼它後面的所有結點都應該沒有子結點。

#include <iostream>
#include <queue>
#include <cstring>
#include <string>
using namespace std;

struct BTree {
    int lchild,rchild;
};
BTree T[25];
bool notRoot[25];
int thisone = -1; // 層序遍歷時當前訪問的節點序數

bool LevelOrder(int root)
{
    queue<int> qt;
    qt.push(root);
    bool nochild = false;
    while (!qt.empty()) {
        thisone = qt.front();
        qt.pop();
        if(T[thisone].lchild!=-1){
            if(nochild)
                return false;
            qt.push(T[thisone].lchild);
        }
        else
            nochild = true;
        if(T[thisone].rchild!=-1){
            if(nochild)
                return false;
            qt.push(T[thisone].rchild);
        }
        else
            nochild = true;
    }
    return true;
}

int GetRootIndex()
{
    int i = 0;
    while (notRoot[i]) {
        ++i;
    }
    return i;
}

int main()
{
    memset(notRoot, 0, sizeof(notRoot));
    int num;
    cin >> num;
    for(int i = 0; i < num; ++i)
    {
        char str[3];
        int temp;
        scanf("%s", str);
        if(str[0] == '-') T[i].lchild = -1;
        else {
            sscanf(str, "%d", &temp);
            T[i].lchild = temp;
            notRoot[temp] = true;
        }

        scanf("%s", str);
        if(str[0] == '-') T[i].rchild = -1;
        else {
            sscanf(str, "%d", &temp);
            T[i].rchild = temp;
            notRoot[temp] = true;
        }

    }

    int rootIndex = GetRootIndex();

    if(LevelOrder(rootIndex))
        cout << "YES" << " " << thisone << endl;
    else
        cout << "NO" << " " << rootIndex << endl;

    return 0;
}