Consider the following Prolog facts and rules: insert(X, L, [X|L]). insert(X, [H|L], [H|L1]) :- insert(X, L, L1). permute([], []). permute([H|T], P) :- permute(T, P1), insert(H, P1, P). Draw the Prolog trees corresponding to the following queries; show the rule and substitution used at each step: (a)  ?- permute([a,b], Y). Y = [a, b] ; Y = [b, a] ; false. (b)  Show the part of the tree with solutions and explain why the tree is infinite: ?- permute(Y, [a,b]). Y = [a, b] ; Y = [b, a] ; ... (c) Explain the effect of the cut in the tree. ?- not(permute(Y, [])). false.

The first step in building a parse tree is to break up the expression string into a list of tokens. There are four different kinds of tokens to consider: left parentheses, right parentheses, operators, and operands. We know that whenever we read a left parenthesis we are starting a new expression, and hence we should create a new tree to correspond to that expression. Conversely, whenever we read a right parenthesis, we have finished an expression. We also know that operands are going to be leaf nodes and children of their operators. Finally, we know that every operator is going to have both a left and a right child.Using the information from above, we can define four rules as follows: 1. If the current token is a '(', add a new node as the left child of the current node, and descend to the left child. 2. If the current token is in the list ['+','-','/','*'], set the root value of the current node to the operator represented by the current token. Add a new node as the right child of…

For words like these, where can you get definitions? Why are they so crucial when it comes to parsing trees?

4. Determine the sentence that represent this parse tree digit 4. digit digit a. (4+5)*3 b. (3+4)*5 c.3*4+5 d. 3*5+4

1. Draw the recursion tree generated when calling hanoi (3, 1, 3). The first parameter is numDisks, the second is the number of the fromPeg, and the last is the toPeg. Each node in the tree should include the function name and three parameters described above. hanoi (3, 1, 3) is the root node in the drawing.

part 1. draw the recursive call tree for the following function when its called with a(7)  int a (int n) { if (n % 4== 0) { return n+1;} else { return a(n-1) + a (n*4); } } part 2. what is the returning value?

Explore the concept of Binary Expression Trees and their role in evaluating mathematical expressions. How can you construct and evaluate expressions using binary expression trees?

2. method. Assume that T(1) (1). Solve the following recurrences using the recursion tree d. T(n) = 4T(n/2) + n e. T(n) = 2T(n-2) +1 f. T(n)= T(n/2) +T(n/3) + n

Solve the binary expression for the numerical answer and draw its respective expression tree   8 7 – 6 5 4 3 + + + 2 1 / * +

L={anbman | n,m=1,2,3....} is given. Draw the derivation tree for the string aaaabbbaaaa.