golang实现n叉树的直径

Understanding N-Ary Trees

N-Ary trees are a type of tree where each node can have an arbitrary number of children. These types of trees are used in a variety of applications such as file systems and data representation. N-Ary trees are similar to binary trees, but instead of having two children, they have multiple children.

Implementing N-Ary Trees in Golang

In Golang, we can implement N-Ary trees using pointers to nodes. Each node can have a slice of pointers to its children. We first define a struct for our node:

```
type Node struct {
val string
children []*Node
}
```

Here, `val` represents the value of the node and `children` is a slice of pointers to child nodes. We can create a new node by simply creating a new instance of the struct:

```
node := &Node{
val: "Parent",
children: []*Node{},
}
```

Once we have created our nodes, we can connect them to form a tree by adding child nodes to the parent node. We can do this by appending a child node to the `children` slice of the parent node:

```
child := &Node{
val: "Child",
children: []*Node{},
}

node.children = append(node.children, child)
```

Finding the Diameter of an N-Ary Tree

The diameter of a tree is the length of the longest path between any two nodes in the tree. In an N-Ary tree, we can find the diameter by first finding the two farthest nodes from the root node. We can do this by performing a depth-first search on the tree and keeping track of the farthest nodes. Once we have found the two farthest nodes, we can find the distance between them by performing another depth-first search, this time between the two nodes.

Here is the code to find the diameter of an N-Ary tree:

```
func diameter(root *Node) int {
farthest1, farthest2 := findFarthestNodes(root)
return findDistance(farthest1, farthest2)
}

func findFarthestNodes(node *Node) (*Node, *Node) {
if node == nil {
return nil, nil
}

var farthest1, farthest2 *Node

for _, child := range node.children {
farthestNode1, farthestNode2 := findFarthestNodes(child)

if farthest1 == nil || len(farthestNode1.val)+1 > len(farthest1.val) {
farthest2 = farthest1
farthest1 = farthestNode1.val + "->" + node.val
} else if farthest2 == nil || len(farthestNode1.val)+1 > len(farthest2.val) {
farthest2 = farthestNode1.val + "->" + node.val
}

if farthest1 == nil || len(farthestNode2.val)+1 > len(farthest1.val) {
farthest2 = farthest1
farthest1 = farthestNode2.val + "->" + node.val
} else if farthest2 == nil || len(farthestNode2.val)+1 > len(farthest2.val) {
farthest2 = farthestNode2.val + "->" + node.val
}
}

return farthest1, farthest2
}

func findDistance(node1, node2 *Node) int {
path1 := strings.Split(node1.val, "->")
path2 := strings.Split(node2.val, "->")

i := 0
for i < len(path1) && i < len(path2) && path1[i] == path2[i] { i++ } return len(path1[i:]) + len(path2[i:])}```

In the `findFarthestNodes` function, we perform a depth-first search on the tree and keep track of the farthest nodes from the root. We do this by recursively calling the function on each child node and comparing their distances to the root. We keep track of the two farthest nodes by checking their distances and updating them accordingly.

In the `findDistance` function, we find the distance between the two farthest nodes. We do this by splitting their paths from the root (which we obtained in the `findFarthestNodes` function) and finding the point where their paths diverge. The distance between the two nodes is then the sum of the lengths of the paths from the divergence point to each node.

Conclusion

In conclusion, we can easily implement N-Ary trees in Golang using pointers to nodes. With these structures, we can then find the diameter of an N-Ary tree by performing a depth-first search to find the two farthest nodes and then computing the distance between them. N-Ary trees are a powerful data structure that can be used in a variety of applications, and Golang provides an easy and efficient way to implement them.