each time we visit node on the left to determine the number of descendents of node vwe compute the difference between the values of the counter when is visited on the left and when it is visited on the rightand add this simple rule gives us the number of descendents of vbecause each node in the subtree rooted at is counted between ' visit on the left and ' visit on the right thereforewe have an ( )-time method for computing the number of descendents of each node another application of the euler tour traversal is to print fully parenthesized arithmetic expression from its expression tree (example algorithm printexpressionshown in code fragment accomplishes this task by performing the following actions in an euler tour"on the leftactionif the node is internalprint "("from belowactionprint the value or operator stored at the node "on the rightactionif the node is internalprint ")code fragment an algorithm for printing the arithmetic expression associated with the subtree of an arithmetic expression tree rooted at the template method pattern