1110 Complete Binary Tree (25分)

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 (≤) 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

完全二叉树的判定，我们可以通过层序遍历，看看有无空缺即可，如果是完全二叉树，打印层序最后一个节点，否则打印第一个。

#include <iostream>
#include <vector>
#include <queue>
using namespace std;
struct node {
    int v;
    string left, right;
}n[30];
int N, root = 0, last;
bool isComplete(int root) {
    queue<int> que;
    que.push(root);
    bool flag = 1, ret = true;
    while(!que.empty()) {
        node tmp = n[que.front()];
        que.pop();
        last = tmp.v;
        if(tmp.left != "-") que.push(stoi(tmp.left));
        if(tmp.right != "-") que.push(stoi(tmp.right));
        if(flag) {
            if(tmp.left != "-" && tmp.right != "-") {
            } else if(tmp.left != "-") {
                flag = 0;
            } else if(tmp.right != "-") {
                ret = false;
            } else {
                flag = 0;
            }
        } else {
            if(tmp.left != "-" || tmp.right != "-") ret = false;
        }
    }
    return ret;
}
int main() {
    cin >> N;
    vector<int> find_root(N, 0);
    for(int i = 0; i < N; i++) {
        n[i].v = i;
        cin >> n[i].left >> n[i].right;
        if(n[i].left != "-") find_root[stoi(n[i].left)] = 1;
        if(n[i].right != "-") find_root[stoi(n[i].right)] = 1;
    }
    while(root < N && find_root[root]) root++;
    bool complete = isComplete(root);
    printf("%s %d\n", complete ? "YES": "NO", complete ? last: root);
    return 0;
}