给定一棵N-Ary树，任务是打印给定N-ary树的所有根到叶路径。
例子：
Input:
1
/ \
2 3
/ / \
4 5 6
/ \
7 8
Output:
1 2 4
1 3 5
1 3 6 7
1 3 6 8
Input:
1
/ | \
2 5 3
/ \ \
4 5 6
Output:
1 2 4
1 2 5
1 5
1 3 6
方法：解决此问题的想法是开始使用深度优先搜索遍历N元树，并不断插入向量中遇到的每个节点，直到遇到叶节点为止。每当遇到叶节点时，都将打印遍历当前根到叶路径的矢量中存储的元素，并删除最后添加的叶并检查下一个组合。
下面是上述方法的实现：
C++
// C++ program for the above approach
#include
using namespace std;
// Strcuture of an N ary tree node
class Node {
public:
int data;
vector child;
// Parameterized Constructor
Node(int x)
: data(x)
{
}
};
// Function to print the root to leaf
// path of the given N-ary Tree
void printPath(vector vec)
{
// Print elements in the vector
for (int ele : vec) {
cout << ele << " ";
}
cout << endl;
}
// Utility function to print all
// root to leaf paths of an Nary Tree
void printAllRootToLeafPaths(
Node* root, vector vec)
{
// If root is null
if (!root)
return;
// Insert current node's
// data into the vector
vec.push_back(root->data);
// If current node is a leaf node
if (root->child.empty()) {
// Print the path
printPath(vec);
// Pop the leaf node
// and return
vec.pop_back();
return;
}
// Recur for all children of
// the current node
for (int i = 0;
i < root->child.size(); i++)
// Recursive Function Call
printAllRootToLeafPaths(
root->child[i], vec);
}
// Function to print root to leaf path
void printAllRootToLeafPaths(Node* root)
{
// If root is null, return
if (!root)
return;
// Stores the root to leaf path
vector vec;
// Utility function call
printAllRootToLeafPaths(root, vec);
}
// Driver Code
int main()
{
// Given N-Ary tree
Node* root = new Node(1);
(root->child).push_back(new Node(2));
(root->child).push_back(new Node(3));
(root->child[0]->child).push_back(new Node(4));
(root->child[1]->child).push_back(new Node(5));
(root->child[1]->child).push_back(new Node(6));
(root->child[1]->child[1]->child)
.push_back(new Node(7));
(root->child[1]->child[1]->child)
.push_back(new Node(8));
// Function Call
printAllRootToLeafPaths(root);
return 0;
} Java
// Java program for the above approach
import java.util.ArrayList;
class GFG
{
// Strcuture of an N ary tree node
static class Node
{
int data;
ArrayList child;
// Parameterized Constructor
public Node(int x)
{
this.data = x;
this.child = new ArrayList<>();
}
};
// Function to print the root to leaf
// path of the given N-ary Tree
static void printPath(ArrayList vec)
{
// Print elements in the vector
for (int ele : vec)
{
System.out.print(ele + " ");
}
System.out.println();
}
// Utility function to print all
// root to leaf paths of an Nary Tree
static void printAllRootToLeafPaths(Node root, ArrayList vec)
{
// If root is null
if (root == null)
return;
// Insert current node's
// data into the vector
vec.add(root.data);
// If current node is a leaf node
if (root.child.isEmpty())
{
// Print the path
printPath(vec);
// Pop the leaf node
// and return
vec.remove(vec.size() - 1);
return;
}
// Recur for all children of
// the current node
for (int i = 0; i < root.child.size(); i++)
// Recursive Function Call
printAllRootToLeafPaths(root.child.get(i), vec);
vec.remove(vec.size() - 1);
}
// Function to print root to leaf path
static void printAllRootToLeafPaths(Node root)
{
// If root is null, return
if (root == null)
return;
// Stores the root to leaf path
ArrayList vec = new ArrayList<>();
// Utility function call
printAllRootToLeafPaths(root, vec);
}
// Driver Code
public static void main(String[] args)
{
// Given N-Ary tree
Node root = new Node(1);
(root.child).add(new Node(2));
(root.child).add(new Node(3));
(root.child.get(0).child).add(new Node(4));
(root.child.get(1).child).add(new Node(5));
(root.child.get(1).child).add(new Node(6));
(root.child.get(1).child.get(1).child).add(new Node(7));
(root.child.get(1).child.get(1).child).add(new Node(8));
// Function Call
printAllRootToLeafPaths(root);
}
}
// This code is contributed by sanjeev2552 Python3
# Python3 program for the above approach
# Strcuture of an N ary tree node
class Node:
def __init__(self, x):
self.data = x
self.child = []
# Function to print the root to leaf
# path of the given N-ary Tree
def printPath(vec):
# Print elements in the vector
for ele in vec:
print(ele, end = " ")
print()
# Utility function to print all
# root to leaf paths of an Nary Tree
def printAllRootToLeafPaths(root):
global vec
# If root is null
if (not root):
return
# Insert current node's
# data into the vector
vec.append(root.data)
# If current node is a leaf node
if (len(root.child) == 0):
# Print the path
printPath(vec)
# Pop the leaf node
# and return
vec.pop()
return
# Recur for all children of
# the current node
for i in range(len(root.child)):
# Recursive Function Call
printAllRootToLeafPaths(root.child[i])
vec.pop()
# Function to print root to leaf path
def printRootToLeafPaths(root):
global vec
# If root is null, return
if (not root):
return
# Utility function call
printAllRootToLeafPaths(root)
# Driver Code
if __name__ == '__main__':
# Given N-Ary tree
vec = []
root = Node(1)
root.child.append(Node(2))
root.child.append(Node(3))
root.child[0].child.append(Node(4))
root.child[1].child.append(Node(5))
root.child[1].child.append(Node(6))
root.child[1].child[1].child.append(Node(7))
root.child[1].child[1].child.append(Node(8))
# Function Call
printRootToLeafPaths(root)
# This code is contributed by mohit kumar 29C#
using System;
using System.Collections.Generic;
// Strcuture of an N ary tree node
public class Node
{
public int data;
public List child;
// Parameterized Constructor
public Node(int x)
{
this.data = x;
this.child = new List();
}
}
public class GFG
{
// Function to print the root to leaf
// path of the given N-ary Tree
static void printPath(List vec)
{
// Print elements in the vector
foreach (int ele in vec)
{
Console.Write(ele + " ");
}
Console.WriteLine();
}
// Utility function to print all
// root to leaf paths of an Nary Tree
static void printAllRootToLeafPaths(Node root, List vec)
{
// If root is null
if (root == null)
return;
// Insert current node's
// data into the vector
vec.Add(root.data);
// If current node is a leaf node
if (root.child.Count == 0)
{
// Print the path
printPath(vec);
// Pop the leaf node
// and return
vec.RemoveAt(vec.Count - 1);
return;
}
// Recur for all children of
// the current node
for (int i = 0; i < root.child.Count; i++)
{
// Recursive Function Call
printAllRootToLeafPaths(root.child[i], vec);
}
vec.RemoveAt(vec.Count - 1);
}
// Function to print root to leaf path
static void printAllRootToLeafPaths(Node root)
{
// If root is null, return
if (root == null)
return;
// Stores the root to leaf path
List vec = new List();
// Utility function call
printAllRootToLeafPaths(root, vec);
}
// Driver Code
static public void Main ()
{
// Given N-Ary tree
Node root = new Node(1);
(root.child).Add(new Node(2));
(root.child).Add(new Node(3));
(root.child[0].child).Add(new Node(4));
(root.child[1].child).Add(new Node(5));
(root.child[1].child).Add(new Node(6));
(root.child[1].child[1].child).Add(new Node(7));
(root.child[1].child[1].child).Add(new Node(8));
// Function Call
printAllRootToLeafPaths(root);
}
}
// This code is contributed by rag2127 输出：
1 2 4
1 3 5
1 3 6 7
1 3 6 8时间复杂度： O(N)
空间复杂度： O(N)