Consider the following algorithm: search(a, first, last, key) 1 if a[first] = key 2 return true 3 if first > = last 4 return false 5 middle = (first + last)/2 6 left = search(a, first, middle, key) 7 right = search(a, middle+1, last, key) 8 return (left or right)write down a recurrence that counts the number of times the comparison in line 1 is performed on an array of length n. write down the asymptotic version of the running time.

Write a program that performs a simple n-body simulation, called "jumping leprechauns." this simulation involves n leprechauns, numberd 1 to n. it maintains a gold value g_i for each leprechaun i, which begins with each leprechaun starting out with a million dollars worth of gold, that is, g_i = 1000000 for each i = 1,. in addition, the simulation also maintains, for each leprachaun,i, a place on the horizon, which is represented as a double-precision floating point number, x_i. in each iteration of the simulation, the simulation processes the leprachauns in order. processing a leprachaun i during its iteration begins by computing a new place on the horizon for i, which is determined by the assignment: