Given the following pseudocode, write the recurrence relation that describes the time complexity of the algorithm. Then, draw a recursion tree for the recurrence relation and solve the recurrence to find the time complexity.

def search$\_$algorithm$($arr$,$ low, high, x$)$:

if high $>=$ low:

mid $=($high $+$ low$)//2$ if arr$[$mid$]==$ x: return mid

elif arr$[$mid$]>$ x:

return search$\_$algorithm$($arr$,$ low, mid $-1,$ x$)$ else:

return search$\_$algorithm$($arr$,$ mid $+1,$ high, x$)$ else: return $-1$