Question $6$

$25$ pts

Consider the clever "divide and conquer" algorithm for the problem of multiplying two n$-$digit numbers described in class. This algorithm breaks the problem into THREE subproblems, where each sub$-$problem has two operands with only half$-$as$-$many digits as in the original two operands.

Illustrate this algorithm for the input values $6241$ and $4589.$

You must DRAW the complete "recursion execution trace tree" for these two inputs. You should assume that the base case is when the two operands have only a single digit each. For each recursive call in the trace$-$tree, you should indicate what are the two parameters sent to that recursive call, and what value is returned by that recursive call, similar to how it was illustrated in the lesson.

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