2. Each exercise below has five parts, as follows: (1) Draw the call tree in the style of Figure 2.30 for the function binCoeff() of Figure 2.28 assuming the given call statement from the main program. (2) Write down the sequence of calls and returns using the indentation notation on page 92. (3) How many times is the function called, including the call from the main program? (4) What is the maximum number of stack frames on the run-time stack during the execution, not counting the frame for the main program? (5) Draw the run-time stack in the style of Figure 2.29 at the given point during execution.

*

(a) Call statement binCoeff(4,1) from the main program. For part (5), draw the run-time stack just before the return from binCoeff(2, 1).

(b) Call statement binCoeff(5,1) from the main program. For part (5), draw the run-time stack just before the return from binCoeff(3, 1).

(c) Call statement binCoeff(3,2) from the main program. For part (5), draw the run-time stack just before the return from binCoeff(1, 0).

(d) Call statement binCoeff(4, 4) from the main program. For part (5), draw the run-time stack just before the return from binCoeff(4,4).

(e) Call statement binCoeff(4, 2) from the main program. For part (5), binCoeff(2, 1) is called twice. Draw the run-time stack just before the return from the second call of the function.