Principles of Programing

To draw the recursion tree for the function `myRecFib(6)`, we need to understand that the Fibonacci sequence is defined by the recurrence relation: $$ F(n) = F(n-1) + F(n-2) $$ with initial conditions: $$ F(0) = 0, \quad F(1) = 1 $$ The given recursive function `myRecFib(n)` computes the Fibonacci numbers with the same recurrence relation. However, the order of evaluation is specified such that `myRecFib(n-2)` is computed before `myRecFib(n-1)`. Let's draw the recursion tree for `myRecFib(6)`: ``` myRecFib(6) | +-- myRecFib(4) | | | +-- myRecFib(2) | | | | | +-- myRecFib(0) | | | | | +-- myRecFib(1) | | | +-- myRecFib(3) | | | +-- myRecFib(1) | | | +-- myRecFib(2) | | | +-- myRecFib(0) | | | +-- myRecFib(1) | +-- myRecFib(5) | +-- myRecFib(3) | | | +-- myRecFib(1) | | | +-- myRecFib(2) | | | +-- myRecFib(0) | | | +-- myRecFib(1) | +-- myRecFib(4) | +-- myRecFib(2) | | | +-- myRecFib(0) | | | +-- myRecFib(1) | +-- myRecFib(3) | +-- myRecFib(1) | +-- myRecFib(2) | +-- myRecFib(0) | +-- myRecFib(1) ``` In this tree, each node represents a call to `myRecFib(n)`. The left child of each node is `myRecFib(n-2)` and the right child is `myRecFib(n-1)`. The tree expands until it reaches the base cases, which are `myRecFib(0)` and `myRecFib(1)`. Notice that there are several repeated calls to the same function with the same arguments (e.g., `myRecFib(2)` and `myRecFib(3)` are each called multiple times). This redundancy is a well-known inefficiency in the naive recursive implementation of the Fibonacci sequence, which can be improved using techniques such as memoization or dynamic programming to avoid redundant calculations.

Math

Consider the recursive function for computing Fibonacci numbers, but with the recursive call in the form: out = myRecFib(n-2) + myRecFib(n-1); Draw the recursion tree for myRecFib(6) assuming the first term in the above expression is evaluated first.

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