PAT-1004 Counting Leaves

1004 Counting Leaves （30 分)

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

Input Specification:

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.The input ends with N being 0. That case must NOT be processed.

Output Specification:

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

算法说明：

算法要求求出每一层没有孩子节点的个数并依次输出，本文采用vector存储结点，当然你可以自己定义结构体。然后用递归计算每一层的没有孩子结点的个数，这时就必须有个数组book[depth]来记录啦，下标代表层数，对应的值表示这一层无孩子结点个数。递归停止的条件为 :vector[index].size()==0 说明当前结点没有孩子结点，使book[depth]++，下面贴出代码。

**树结构与vector存储**
```c++
// 1004 Counting Leaves.cpp : Defines the entry point for the console application.
//

include "stdafx.h"

include

include

using namespace std;

vector vec[100];

int maxDepth=-1;

int book[100]={0};

/**

4 2

01 2 02 03

02 1 04

*/

void dfs(int index,int depth){

if(vec[index].size()==0){

book[depth]++;

if(depth>maxDepth)

maxDepth=depth;

return;

}

for(int i=0;i<vec[index].size();i++)

dfs(vec[index].at(i),depth+1);

}

int main(int argc, char argv[])

{

int N,M,node,k,leaf;

cin >>N>>M;

for(int i=0;i<M;i++){

cin >>node>>k;

for(int j=0;j<k;j++){

cin >> leaf;

vec[node].push_back(leaf);

}

}

dfs(1,0);

cout<<book[0];

for(int j=1;j<=maxDepth;j++){

cout<<" "<<book[j];

}

return 0;

}

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