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 Java DSA implementation can be compared directly with the rest of the DSA track.

Basic Implementation

Basic.java 
import java.util.*;

public class Basic {
    static class Node {
        int value;
        Node left;
        Node right;
        Node(int value) { this.value = value; }
        Node(int value, Node left, Node right) { this.value = value; this.left = left; this.right = right; }
    }
    static String render(Node node) {
        if (node == null) return "_";
        if (node.left == null && node.right == null) return Integer.toString(node.value);
        return node.value + "(" + render(node.left) + "," + render(node.right) + ")";
    }
    static Node sampleTree() {
        return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));
    }
    static Node insert(Node root, int value) { if (root == null) return new Node(value); if (value < root.value) root.left = insert(root.left, value); else root.right = insert(root.right, value); return root; }
    public static void main(String[] args) { Node root = null; for (int value : new int[] {4, 2, 6, 1, 3, 5, 7}) root = insert(root, value); System.out.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.