just need part B Draw a recursion tree diagram for Tn 4Tn4

just need part B

Draw a recursion tree diagram for T(n) ={ 4T(n/4) + n if n>-2 1 if n=1. Use it to find the exact solution to the recurrence, assuming n is a power of 4.

Solution

b) The function is one-one if no two images of the LHS mapped to the same value on the right

Let us G(x1,y1) = (2y1,-x1) and G(x2,y2) = (2y2,-x2)

2y1 = 2y2 and -x1 = -x2

It implies that y1 = y2 and x1 = x2

Hence the function is one-one since one (x,y) is mapping to only one possible pair value

ii) The function is onto since it covers the entire range of RXR, because we can generate any pair using the value of x and y to map to the point (2y,-x)

Hence the function is onto

Therefore, the function is both one-one and onto