[PAT甲级]1004. Counting Leaves (30)(求树各层非叶子节点数目)_八叉树非叶子节点的子节点数目-优快云博客

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1004. Counting Leaves (30)

A family hierarchy is usually presented by a pedigree tree. Your job is to count those family members who have no child.

Input
Each input file contains one test case. Each case starts with a line containing 0 < N < 100, the number of nodes in a tree, and M (< N), the number of non-leaf nodes. Then M lines follow, each in the format:

ID K ID[1] ID[2] … ID[K]
where ID is a two-digit number representing a given non-leaf node, K is the number of its children, followed by a sequence of two-digit ID’s of its children. For the sake of simplicity, let us fix the root ID to be 01.

Output
For each test case, you are supposed to count those family members who have no child for every seniority level starting from the root. The numbers must be printed in a line, separated by a space, and there must be no extra space at the end of each line.

The sample case represents a tree with only 2 nodes, where 01 is the root and 02 is its only child. Hence on the root 01 level, there is 0 leaf node; and on the next level, there is 1 leaf node. Then we should output “0 1” in a line.

Sample Input

2 1
01 1 02

Sample Output

0 1

题目大意：

输入第一行给出树的结点个数n和非叶子结点m
接下来输入m行每行给出非叶子结点id, 结点id的孩子个数k, k个孩子结点的id
最后输出每一层叶子结点的个数
如果题目给的例子不明显的话，我再举个例子

输入

输出

0 0 2 1 1

举例的树

      01  
    /     \
   02     03
  /      /  \
 04     05  06
       /  \
     07   08
          / 
        09

思路：

我用的深度优先遍历递归算法
定义二维数组arr 存储各个结点的孩子
定义数组res 存储各层叶子结点数目从0开始计数
定义maxDepth为最大深度从1开始计数
从根节点开始遍历，直到遇到叶子结点，将当前层res[depth]++ ，更新最大深度maxDepth，最后输出

代码：

#include <iostream>
#include <vector>
using namespace std;
void dfs(vector<vector<int>>& arr, int (&res)[100], int &maxDepth, int index, int depth){
    if(arr[index].size() == 0){
        res[depth]++;
        maxDepth = maxDepth>depth ? maxDepth : depth;
        return;
    }
    for(int i=0; i<arr[index].size(); i++)
        dfs(arr, res, maxDepth, arr[index][i], depth+1);
}
int main()
{
    vector<vector<int>> arr(100);//存储各个结点的孩子
    int res[100] = {0};//存储各层叶子结点数目
    int maxDepth = 0;//最大深度 从1开始计数
    int n, m;
    cin >> n >> m;
    for(int i=0; i<m; i++){
        int id,k;
        cin >> id >> k;
        for(int j=1; j<=k; j++){
            int temp;
            cin >> temp;
            arr[id].push_back(temp);
        }
    }
    dfs(arr, res, maxDepth, 1, 0);// 1表示根节点id, 0表示当前层是第0层
    cout << res[0];
    for(int i=1; i<=maxDepth; i++)
        cout << " " << res[i];
    return 0;
}