Select all the true statements: A) If lim, 0 f(n)/g(n) = 0 then f(n) = 0(g(n)), B) If lim,00 f(n)/g(n) = 42 then f(n) = 0(g(n)). %3D %3D C) It is always true that if f(n) = 0(g(n)) then f(n) = 0(g(n)). %3D D) If f(n) = 100g(n) then f(n) = O((n)). %3D O A O-C
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- Given the following FSM M, the correct statements are: D 2 0 a 93 b a (a u ba)bb*a is a regular expression that generates L(M). (€ U b)a(bb*a)* is a regular expression that generates L(M). ba U ab*a is a regular expression that generate L(M). (a Uba)(bb*a)* is a regular expression that generate L(M).The following function f uses recursion:def f(n):if n <= 1return nelse 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 <- 0b <- 1 if n = 0return aelsif n = 1 return belsefor i in 1..nc <- a + b a <- b b <- c return bb) def f(n):a <- 0i <- n while i > 0 a <- a + i + (i-1) return ac) def f(n): arr[0] <- 0 arr[1] <- 1 if n <= 1return arr[n]elsefor 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 <= 1return arr[n]elsea <- 0 for i in 0..n a <- a + arr[i]return aThe 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
- Design the following LCG random number generators by choosing the following parameters ( a, c, m, and Zo ) carefully and writing the recursive formula for each of the following: a . LCG1: has Zo = 17. b. LCG2 : has 128 > m > 16 LCG3 : has c = 7 d . LCG4: has a = 7 e. LCG5: has c not equal to 3 C.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 ъ <-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 bFind X(z) for the sequence x(n) =(a)" u(n) Note1: a, n must be defined as symbolic variables Note2: Use disp() function instead of pretty() Note3: You should write the code and the result
- Compute f(6) for the recursive function below. def f(n): if n == 0: return 1 if n == 1: return 2 else: return f(n-1)+n*f(n-2)-nFactorial of a number is defined as: n! = n(n-1)(n-2)(n-3)...(2)(1) For example, 4! = 4*3*2*1 The n! can be written in terms of (n-1)! as: n! = n* (n-1)! (n-1)! = (n-1)*(n-2) ! and so forth. Thus, in order to compute n!, we need (n-1)!, to have (n-1)!, we need (n-2)! and so forth. As you may immediately notice, the base case for factorial is 1 because 1! = 1. Write a program that uses a recursive function called factorial that takes an integer n as its argument and returns n! to the main. C++ PLEASEWrite a recursive function F(N) that generalízes the following function: NF(N) 1 2 10 19 4 37 5 70 (Hìnt: F(N) computes the output differently for odd and even values of N! Think about the base case first, then think about what would be the recursive case for the odd value of N and what would be the recursive case for an even value of N!) For example: Test Result print(F(0)) 1 Answer: (penalty regime: 0, 0, 0, 0, 0, 5, 10, 15, 20, .. %)
- 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 aThe following function f uses recursion:def f(n):if n <= 1return nelsereturn f(n-1) + f(n-2)5Let 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 <- 0b <- 1if n = 0return aelsif n = 1return belsefor i in 1..nc <- a + ba <- bb <- creturn b b) def f(n):a <- 0i <- nwhile i > 0a <- a + i + (i-1)return a c) def f(n):arr[0] <- 0arr[1] <- 1if n <= 1return arr[n]elsefor i in 2..narr[i] <- arr[i-1] + arr[i-2]return arr[n] d) def f(n):arr[0..n] <- [0, ..., n]if n <= 1return arr[n]elsea <- 0for i in 0..na <- a + arr[i]return aa) Write a recursive method that calculates the following series: F(n)= (n1+i)ni=1*(n2+i)n/2i=1*(n4+i)n/4i=1*(n8+i)n/8i=1*....*2 b) Write the recurrence expression T(n).