Find time and space complextity of the following code.

public class MaxPathSumBinaryTree {

public int maxPathSum(TreeNode root) {

//wrap a global variable into an array so that we can change the value//

int[] max = new int[] {Integer.MIN_VALUE};

maxSumHelper(root, max);

return max[0];

}

private int maxSumHelper(TreeNode root, int[] max) {

if (root == null) {

return 0;

}

int left = maxSumHelper(root.left, max);

int right = maxSumHelper(root.right, max);

//when root node has both left and right child, we need to update the max path sum//

if (root.left != null && root.right != null) {

max[0] = Math.max(max[0], left + right + root.key);

return Math.max(left, right) +root.key;

}

return root.left == null?right + root.key : left + root.key;

}

}