543. Diameter of Binary Tree

class Solution {
    private static class State {
        private int maxNodes = 1;
    }

    public int diameterOfBinaryTree(TreeNode root) {
        State state = new State();
        maxDepth(root, state);
        return state.maxNodes - 1;
    }

    private int maxDepth(TreeNode node, State state) {
        if (node == null) {
            return 0;
        }

        int leftMaxDepth = maxDepth(node.left, state);
        int rightMaxDepth = maxDepth(node.right, state);

        int maxNodes = leftMaxDepth + 1 + rightMaxDepth;
        state.maxNodes = Math.max(state.maxNodes, maxNodes);
        return Math.max(leftMaxDepth, rightMaxDepth) + 1;
    }
}

References

543. Diameter of Binary Tree