Construct an expression tree for the expression a +( bc )* d +( e * f)

Answer: Taking "bc" as \(b \times c\), the expression is \(\big(a + ((b*c)*d)\big) + (e*f)\), so the root is the last + and the tree is:

              +
            /   \
          +       *
         / \     / \
        a   *   e   f
           / \
          *   d
         / \
        b   c

How to build it

1. In an expression tree, operands are leaves and operators are internal nodes. The operator applied last becomes the root.
2. Apply precedence: * is done before +, and operators of equal precedence go left to right. So \((b*c)*d\) and \((e*f)\) are worked out first.
3. The two + signs are then applied left to right: first \(a + ((b*c)*d)\), then that result \(+ (e*f)\). So the second + is the root.
4. Left subtree of the root: + with children \(a\) and \((b*c)*d\). Right subtree: * with children \(e\) and \(f\).

Check: the postorder traversal of this tree gives the postfix form a b c * d * + e f * +, which evaluates the expression correctly.