Which of the following are admissible, given admissible heuristics h1, h2? Which of the following are consistent, given consistent heuristics h1, h2? Justify your answer.
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Which of the following are admissible, given admissible heuristics h1, h2? Which of the following are consistent, given consistent heuristics h1, h2? Justify your answer.
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- Using foldl, define a function num2int :: [Int] -> Int -> Int that converts a list of numbers and the number n into an integer of base n. >num2int [3,4,5,6] 10 3456 >num2int [1,1,0,1,0,0,0,1,0,1,0,1,1,0] 2 3456 num2int :: [Int] -> Int -> Int num2int x y = foldl (\acc (a,b) -> ___a___ + b*y^a) 0 (___b___ (\x y ->(x,y)) [0..] (___c___ x)) fill in blank spaces of a , b , and cWrite Algorithm to Conversion from an Arabic number to a modern Roman number.in: decimal number n (0 ≤ n)out: sequence R = s0, s1,...,s12 representing the structure of the Roman number (Ri = number of primitives Vi in n for i ∈ [0, 12])constant: sequence P = 1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1 of primitive Roman numberslocal: remainder x to be converted (0 ≤ x ≤ n); coefficient c for a primitive Romannumbers (for other than P0, 0 ≤ c ≤ 3)A number of the form a + ib, in which i2 = -1 and a and b are real numbers, is called a complex number. We call the real part and b the imaginary part of a + ib. Complex numbers can also be represented as ordered pairs (a, b). The addition and multiplication of complex numbers are defined by the following rules: (a + ib) + (c + id) = (a + c) + i(b + d ) (a + ib) * (c + id) = (ac - bd) + i(ad + bc) Using the ordered pair notation, these rules are written as: (a, b) + (c, d) = ((a + c), (b + d )) (a, b) * (c, d) = ((ac - bd ), (ad + bc)) C++ has no built-in data type that allows us to manipulate complex numbers. Construct a data type, complex Type, that can be used to process complex numbers. Overload the stream insertion and stream extraction operators for easy input and output. We will also overload the operators + and * to perform addition and multiplication of complex numbers. If x and y are complex numbers, we can evaluate expressions such as x + y and x * y.
- True or false set{(x,x2):x∈Z}canbeseeasafunctionZ→Q. set{(x2,x):x∈Z}canbeseeasafunctionZ→Q.Find f(1), f(2), f(3), f(4), and f(5) if f(n) is defined re-cursively by f(0) = 3 and for n = 0, 1, 2, ... a) f(n + 1) = −2f(n).b) f(n + 1) = 3f(n) + 7.Write Python Code Farmer John is worried for the health of his cows after an outbreak of the highly contagious bovine disease COWVID-19.In order to limit transmission of the disease, Farmer John's N cows ( 2<=N<=105) have decided to practice "social distancing" and spread themselves out across the farm. The farm is shaped like a 1D number line, with M mutually-disjoint intervals (1<=M<=105) in which there is grass for grazing. The cows want to locate themselves at distinct integer points, each covered in grass, so as to maximize the value of D, where D represents the distance between the closest pair of cows. Please help the cows determine the largest possible value of D. INPUT FORMAT (file socdist.in): The first line of input contains N and M. The next M lines each describe an interval in terms of two integers a and b, where 0<=a<=b<=1018. No two intervals overlap or touch at their endpoints. A cow standing on the endpoint of an interval counts as standing on…
- Describe each of the following sets by listing its elements:a. {x | x ∈ N and x2 − 5x + 6 = 0}b. {x | x ∈ R and x2 = 19}c. {x | x ∈ N and x2 − 2x − 8 = 0}}d. {x | x ∈ Z and x ∗ x = 4}0o.9. """n a positive integer N, find and return the longest distance between twoconsecutive 1' in the binary representation of N.If there are not two consecutive 1's, return 0 For example:Input: 22Output: 2Explanation:22 in binary is 10110In the binary representation of 22, there are three ones, and two consecutive pairs of 1's.The first consecutive pair of 1's have distance 2.The second consecutive pair of 1's have distance 1.The answer is the largest of these two distances, which is 2""" # 原方法为 binary_gap，但通过实验发现算法有误，不论是什么数，输出值最多为2。# 改进方法为binary_gap_improved。# The original method is binary_gap,# but the experimental results show that the algorithm seems to be wrong,# regardless of the number, the output value is up to 2.# The improved method is binary_gap_improved.def binary_gap(N):.Not pseudocode Suppose the economies of the world use a set of currencies C1, . . . , Cn; think of these as dollars, pounds, Bitcoin, etc. Your bank allows you to trade each currency Ci for any other currency Cj, and finds some way to charge you for this service. Suppose that for each ordered pair of currencies (Ci, Cj ), the bank charges a flat fee of fij > 0 dollars to exchange Ci for Cj (regardless of the quantity of currency being exchanged). Describe an algorithm which, given a starting currency Cs, a target currency Ct, and a list of fees fij for all i, j ∈ {1, . . . , n}, computes the cheapest way (that is, incurring the least in fees) to exchange all of our currency in Cs into currency Ct. Also, justify the its runtime. [We are expecting a description of the algorithm, as well as a brief justification of its runtime.]
- The following function f uses recursion: def f(n): if n <= 1 return n else return f(n-1) + f(n-2) Let n be a valid input, i.e., a natural number. Which of the following functions returns the same result but without recursion? a) def f(n): a <- 0 b <- 1 if n = 0 return a elsif n = 1 return b else for i in 1..n c <- a + b a <- b b <- c return b b) def f(n): a <- 0 i <- n while i > 0 a <- a + i + (i-1) return a c) def f(n): arr[0] <- 0 arr[1] <- 1 if n <= 1 return arr[n] else for i in 2..n arr[i] <- arr[i-1] + arr[i-2] return arr[n] d) def f(n): arr[0..n] <- [0, ..., n] if n <= 1 return arr[n] else a <- 0 for i in 0..n a <- a + arr[i] return aIn C language, write a simple substitution code for an alphabetic string. That is, declare a permutation of the 26 alphabetic characters i.e. char perm[] = “qjczieaungsdfxmphybklortvw” Now, given a message string e.g. char msg[] = “secret message to encode”; Replace all occurrences of ‘a’ with ‘q’ (since perm[0]=’q’) Replace all occurrences of ‘b’ with ‘j’ (since perm[1]=’j’) Replace all occurrences of ‘z’ with ‘w’ (since perm[25]=’w’)So that, the message is modified to “bicyik fibbqai km ixcmzi” This programme should only convert lowercase letters. Any input character that is not a lowercase letter should be left unchanged.The following function f uses recursion: def f(n): if n <= 1 return n else return f(n-1) + f(n-2) 5 Let n be a valid input, i.e., a natural number. Which of the following functions returns the same result but without recursion? a) def f(n): a <- 0 b <- 1 if n = 0 return a elsif n = 1 return b else for i in 1..n c <- a + b a <- b b <- c return b f(n): a <- 0 i <- n while i > 0 a <- a + i + (i-1) return a f(n): arr[0] <- 0 arr[1] <- 1 if n <= 1 return arr[n] else for i in 2..n arr[i] <- arr[i-1] + arr[i-2] return arr[n] f(n): arr[0..n] <- [0, ..., n] if n <= 1 return arr[n] else a <- 0 for i in 0..n a <- a + arr[i] return a