Tree Diameter

The diameter of a tree (sometimes called the width) is the number of nodes on the longest path between two leaves in the tree.

The diameter of a tree T is the largest of the following quantities:

* the diameter of T’s left subtree
* the diameter of T’s right subtree
* the longest path between leaves that goes through the root of T (this can be computed from the heights of the subtrees of T)

package Tree;

/*
 * The diameter of a tree is the Number of Nodes on the longest path between two leaves in the tree.
 */

public class DiameterBT {
    class TreeNode {
        int val;
        TreeNode left, right;
        public TreeNode(int val) {
            this.val = val;
        }
    }
    /*
     * Time : O(n log n)
     * Space : O(log n)
     */
    public int diameter(TreeNode root) {
        if (root == null) return 0;
        int dial = diameter(root.left);
        int diar = diameter(root.right);
        int hl = height(root.left);
        int hr = height(root.right);
        return Math.max(hl + hr + 1, Math.max(dial, diar));
    }
    public int height(TreeNode root) {
        if (root == null) return 0;
        return Math.max(height(root.left), height(root.right)) + 1;
    }
    
    /*
     * Time : O(n)
     */
    class Height {
        public int val;
    }
    public int diameter(TreeNode root, Height height) {
        if (root == null) {
            height.val = 0;
            return 0;
        }
        Height hl = new Height();
        Height hr = new Height();
        int dl = diameter(root.left, hl);
        int dr = diameter(root.right, hr);
        height.val = Math.max(hl.val, hr.val) + 1;
        return Math.max(hl.val + hr.val + 1, Math.max(dl, dr));
    }
    
    public static void main(String[] args) {
        DiameterBT sol = new DiameterBT();
        TreeNode node0 = sol.new TreeNode(1);
        TreeNode node1 = sol.new TreeNode(2);
        TreeNode node2 = sol.new TreeNode(3);
        TreeNode node3 = sol.new TreeNode(4);
        TreeNode node4 = sol.new TreeNode(5);
        node0.left = node1; node0.right = node2;
        node1.left = node3; node1.right = node4;
        System.out.println(sol.diameter(node0));
        System.out.println(sol.diameter(node0, sol.new Height()));
    }
}