Expand each of the following summation. one term for each Value of R. Simplify each term as For example, enter 1 + 4 +9 instead of 12 +22 +32 or 14. 8 1) Σ 2* k=0 = 0 2 Σ 12 - k=2 Sacr as pos
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- Write 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)To represent an integer value of n in decimal, we need to use ⌈log10(n + 1)⌉ digits . Verify this using n = 35, 1290. Note that for any real number x, ⌈x⌉ is the smallest integer that is greater than x, this means we always round up. For example, ⌈10.3⌉ = 11, ⌈−5.2⌉ = −5. To represent an intege value of n in binary, we need to use ⌈log2(n + 1)⌉ binary digits . Verify this using n = 35, 1290. Use the definition of logarithmic function to show that log2n / log10n = log210Suppose that you are given the following logical statement:¬ P ∧ Q → ¬ R ∨ SBased on our discussion of order of operations, which is the correct way to interpretthis?(a) ¬(P ∧ ((Q → (¬R)) ∨ S))(b) (¬(P ∧ (Q → (¬R)))) ∨ S(c) ((¬P) ∧ (Q → (¬R))) ∨ S(d) (¬P) ∧ ((Q → (¬R)) ∨ S)(e) (¬(P ∧ Q)) → (¬(R ∨ S))(f) ((¬P) ∧ Q) → ((¬R) ∨ S)(g) ((¬P) ∧ (Q → (¬R))) ∨ S(h) ((¬P) ∧ (Q → (¬R))) ∨ S(i) (¬P) ∧ ((Q → (¬R)) ∨ S)(j) ¬((P ∧ Q) → (¬(R ∨ S)))
- please answer the following A) d(n) is O(F(n)) and f(n) is O(g(n) ) show that d(n) is O(g(n)) B) show that n^3 long is omega(n^3) C) show that (summation symbol) n, i = 1 i^2 is O(n^3)2022-02-14 20:52:35 Write the primitive counting results for your 40 sheep: 40= For example, the answer for "14" would be (1,1,1,0), meaning that the first division of sheep had none left over, but every other division of sheep had a leftover sheep. Include the commas and the parentheses in your answer.Count consecutive summers def count_consecutive_summers(n): Like a majestic wild horse waiting for the rugged hero to tame it, positive integers can be broken down as sums of consecutive positive integers in various ways. For example, the integer 42 often used as placeholder in this kind of discussions can be broken down into such a sum in four different ways: (a) 3 + 4 + 5 + 6 + 7 + 8 + 9, (b) 9 + 10 + 11 + 12, (c) 13 + 14 + 15 and (d) 42. As the last solution (d) shows, any positive integer can always be trivially expressed as a singleton sum that consists of that integer alone. Given a positive integer n, determine how many different ways it can be expressed as a sum of consecutive positive integers, and return that count. The number of ways that a positive integer n can be represented as a sum of consecutive integers is called its politeness, and can also be computed by tallying up the number of odd divisors of that number. However, note that the linked Wikipedia de0inition…
- Please explain Crime Wave more clearly for me please there's a picture of the decription and also please comment on each line if possible on the code below to for me to have a better understanding of what each line is doing. It is in C++. Please also give the space and time complexity and the reason why. #include <stdio.h>#include <string.h>#include <math.h>#define eps 1e-6double W[105][105];int N, M;int mx[105], my[105]; // match arrdouble lx[105], ly[105]; // label arrint x[105], y[105]; // used arrint hungary(int nd) { int i; x[nd] = 1; for(i = 1; i <= M; i++) { if(y[i] == 0 && fabs(W[nd][i]-lx[nd]-ly[i]) < eps) { y[i] = 1; if(my[i] == 0 || hungary(my[i])) { my[i] = nd; return 1; } } } return 0;}double KM() { int i, j, k; double d; memset(mx, 0, sizeof(mx)); memset(my, 0, sizeof(my)); memset(lx, 0, sizeof(lx)); memset(ly, 0, sizeof(ly));…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 aI need help with this question of Data Structures and Algorithmns 1) True or False a) If g1(n) = O(f1(n)) and g2(n) = O(f2(n)), then g1 x g2 = O(f1(n) x f2(n)) (True or False) b) If f(n) = logan and g(n) = logbn , then f(n) = Θ(g(n)) (True or False)
- 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 aDetermine how many additions are done in the worst case scenario of the following code. Assume that all variables are properly declared. y = 1; for (i=1; i<=n;i++) { for (j = 1; j<=n;j++) { x = i + j; x = x * y; } x = y + x; }Consider a base 26 number system wherein the letters of the alphabet are the digits. That is, A=0, B=1, C=2, … Z=25 in base 10. Use the MAL as a number in the base 26 system, and KHA as another number in the base 26 system.Add these numbers together to obtain the sum in based 26. Example 1 — if your first name is “Peter” and your surname is “Pan”, then add up PET26 and PAN26, and show the sum in base 26.Example 2 — if your first name is “Peter” and your surname is “Pa”, then add up PET26 and PAA26, and show the sum in base 26.