Trees

BST Insert

Insert values into a binary search tree by comparing at each node.

Algorithm

The canonical tree is 4(2(1,3),6(5,7)), so this Go DSA implementation can be compared directly with the rest of the DSA track.

Basic Implementation

basic.go 
package main

import (
    "fmt"
    "strings"
)

type Node struct { value int; left *Node; right *Node }
func render(node *Node) string {
    if node == nil { return "_" }
    if node.left == nil && node.right == nil { return fmt.Sprintf("%d", node.value) }
    return fmt.Sprintf("%d(%s,%s)", node.value, render(node.left), render(node.right))
}
func sampleTree() *Node {
    return &Node{4, &Node{2, &Node{1, nil, nil}, &Node{3, nil, nil}}, &Node{6, &Node{5, nil, nil}, &Node{7, nil, nil}}}
}
func listString(values []int) string {
    parts := []string{}
    for _, value := range values { parts = append(parts, fmt.Sprintf("%d", value)) }
    return "[" + strings.Join(parts, ", ") + "]"
}
func insert(root *Node, value int) *Node { if root == nil { return &Node{value: value} }; if value < root.value { root.left = insert(root.left, value) } else { root.right = insert(root.right, value) }; return root }
func main() { var root *Node; for _, value := range []int{4, 2, 6, 1, 3, 5, 7} { root = insert(root, value) }; fmt.Println(render(root)) }

Complexity

  • Time: O(h) per insert
  • Space: O(n)

Implementation notes

  • Render tree structure explicitly instead of printing node objects.
  • The replay highlights the node, traversal state, queue, path, or search cursor that changes at each step.
binary search tree Values smaller than a node go left; larger values go right.