Consider the following recurrence algorithm Algorithm 1 REVERSE 1.  function REVERSE(A) 2.        if |A| = 1 then 3.              return A 4.                else 5.                    Let B and C be the first and second half of A 6.                    return concatenate REVERSE(C) and REVERSE(B) 7.                 end if 8.            end function Let T(n) be the running time of the algorithm on an instance of size n. Write down the recurrence relation for T(n) and solve it

Algorithm Binary Search Input:  L = a1, a2, ... , an list of distinct integers; x integer Output: p integer i = 1; j = n; found = F; p = 0; while i ≤ j and found = F   m = ⌊i+j2⌋; if am = x then found = T and p = m             else if am < x then i = m + 1                                    else j = m - 1; return p; When performing Algorithm Binary Search with input  L = 1,3,5,7,9,11,13 and x = 9, how many times is x compared to an element ai of the list L?

Make AST Nodes: IfNode, WhileNode, RepeatNode. All will have BooleanCompare for a condition and a collection of StatementNode. ForNode will have a Node for from and a node for to. This will have to be of type Node because it could be any expression. For example: for a from 1+1 to c-6  Make parsing functions for each. Java won't let you create methods called if(), etc. parseIf() is an example of a way around that; use whatever you like but use good sense in your names.  Next let's look at function calls. Each function has a name and a collection of parameters. A parameter can be a VAR variable  or something that came from booleanCompare (IntegerNode, VariableReferenceNode, etc). It would be reasonable to make 2 objects - ParameterVariableNode and ParameterExpressionNode. But for this very simple and well-defined case, we can do something simple: ParameterNode has a VariableReferenceNode (for VAR IDENTIFIER) and a Node for the case where the parameter is not a VAR.    One more thing -…

Why does binary search take less time than linear search, and what variables lead to this reduction? It would be helpful if you explained your actions.