Consider this evaluation function for Chess: 9* (QWQB) + 5*(RW - RB) + 3*(KW - KB) + 3*(BW - BB) + 1*(PW - PB) where: QW denotes the number of Queens that White has, QB denotes the number of Queens that Black has, and so on (the shapes and letters for pieces are shown below). ด KING QUEEN BISHOP KNIGHT ROOK PAWN Q B K R P Calculate the evaluation function value for the following game state: 1 ♡ 7
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- Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solutions including original diagram for part a!Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solution!This problem exercises the basic concepts of game playing, using tic-tac-toe (noughtsand crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3 = 1 and −1 to any position with O3 = 1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval (s) = 3X2(s)+X1(s)−(3O2(s)+O1(s))."Mark on your tree the evaluations of all the positions at depth 2."
- Now, we'll instead use sklearn's train_test_split() function here to define our train and test set. Store train data (predictors) into MR_train_X and labels (outcomes) into MR_train_Y. Similarly, store test data into MR_test_X and test labels into MR_test_Y. In addition to providing the predictors (MR_X) and outcomes (MR_Y) to the function, we will use the following arguments for this task: test_size: 0.2 random_state: 200Consider the functionf :: Int -> Intf n = if n==0then 0else 1 + (f(n-1))Use induction to show that the function f returns the value of n for all possible inputs n ≥0.Here are the steps:1. Verify that f 0 returns 0 to show the base case.2. Show that if f(n-1) returns n −1 then f n returns n.3. Since you have shown the base case and the induction step, you can confidentlystate that the function works for all possible nonnegative input values.Hint: To show that ”if f(n-1) returns n −1 then f n returns n” is valid you need toassume that f(n-1) returns n −1 and then argue that it must follow that f n returnsn. Use the definition of the function and just a little bit of algebra.Criteria for Success: You have clearly written down all three steps of the inductive proof. Your proof contains complete sentences which explain all the steps andthe algebra. I don’t want to see just a bunch of symbols on a page!Suppose we have the function g(n) = 2n - n . Below are a number of statements regarding how the feature grows depending on n. D True C,D True A true no on is true
- Note that for this question, you can in addition use ``land'' for the symbol ∧ ``lor'' for the symbol ∨ ``lnot'' for the symbol ¬. Given the following three sentences:A) Every mathematician is married to an engineer.B) A bachelor is not married to anyone.C) If George is a mathematician, then he is not a bachelor. a) Convert A,B,C into three FOL sentences, whereMn(x): x is a mathematician.Er(x): x is an engineer.Md(x,y): x is married to y.Br(x): x is a bachelor.george: George is a constant. b) Show that A does-not-entail C. (Hint: Consider defining an interpretation I such that I models A, but does-not-model C.)c) Show that {A,B} entails C. (Hint: For a given interpretation I, consider two difference cases, the case where Mn(george) is true, and the case Mn(george) is false. For both cases, argue that it is always that I models C).d) Convert A,B, lnot C into a set of clausal forms, number your clauses. (Note that C is negated here!) e) Derive the empty clause from the set of clauses…The Family of Logarithmic Functions Write a Learning Log entry about the family of functions y = logb(x). Include the descriptive statements your team has come up with and any others that you think should be added from the class discussion. As you write, think about which statements are very clear to you and which need further clarification.Write a Matlab function that will: read in the spreadsheet file, accept two textual/string arguments: first metric abbreviation/acronym (for example GP) from the list above, Second metric abbreviation/acronym (for example 3P%) from the list above, finds the player (A) who has the highest/maximum value of the FIRST METRIC (if there is more than one with that value, pick the first one - lowest row number) and stores his name and corresponding FIRST METRIC value, finds the player (B) who has the lowest/minimum value of the FIRST METRIC (if there is more than one with that value, pick the first one - lowest row number) and stores his name and corresponding FIRST METRIC value, computes FIRST METRIC average for all players, finds SECOND METRIC value for both players found above, computes SECOND METRIC average for all players,
- The binomial coefficient C(N,k) can be defined recursively as follows: C(N,0) = 1, C(N,N) = 1, and for 0 < k < N, C(N,k) = C(N-1,k) + C(N - 1,k - 1). Write a function and give an analysis of the running time to compute the binomial coefficients as follows: A. The function is written using dynamic programming.Consider the function, f(n), defined by the following code int f(int n) { int r = 0; if ( n % 2 == 0 ) return 1; // when n is even while ( n > 1 ) { n = n – 3; r++; } return r; } From the definitions of big-Theta and little-oh: Prove or disprove that f(n) is Θ ( n ) 2. Prove or disprove that f(n) is o ( n^2 ) ( note: function f(n) as defined by the code, that is, the return value, and is not asking about the runtime of the code.)Project 1 dealt with single symbol Huffman Coding. Project 2 deals with Extended Huffman Codes. For instance, for a source emitting two symbols A and B, the second order extension involves coding messages AA, AB, BA and BB (22 in number). The third order extension involves messages such as AAA, AAB, etc. (23 in number). The probabilities of such strings are computed by multiplying the individual probabilities. For this project, use the Matlab code you have developed in Project 1 to perform third, fourth and fifth order extensions of a source message. 1. Choose an alphabet a set of at least six (6) symbols with assigned probabilities. 2. Compute the third, fourth and fifth order extension probabilities. 3. Using the built-in algorithm, derive the Huffman Code for each extension. 4. Compute the following quantities: (i) Average length of the codeword; (ii) The code efficiency; (iii) The Compression Ratio; (iv) Speed of computation.