Suppose that G(x) = B0 + B1*x + B2*x^2 + B3*x^3 + B4*x^4 + .... Suppose that G'(x) = F(x). What is B50?
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8.
Suppose that
G(x) = B0 + B1*x + B2*x^2 + B3*x^3 + B4*x^4 + ....
Suppose that G'(x) = F(x). What is B50?
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- 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. [A description or pseudocode (either is OK) of the algorithm, as well as a brief justification of its runtime.]Let A = {1, 2, 3, 4, 5} and B = {2, 3, 4, 5, 6, 7} and C = {a, b, c, d, e} 15. Give an example of f: A -> B that is not 1-1.T=4, n=12 and A=(3,5,8,8,9,16,29,41,50,63,64,67). Draw the corresponding walkthrough as shown in P.146.
- Q3) Let Σ = {a , b}. Find DFA's for: d) L = { wab: w€ {a,b}*}e) L = { abwab: w€ {a,b}*}f) L = { ab5wb4 : w € {a,b}* }Given X = {1, 2, 5, 8, 9}, Y = {3, 4, 6, 7, 8}, Z = {1, 2, 4, 6, 8} and U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Findthe following: 1. (X -Z̅) ∪ Y2. (X̅ ∪ Z) ∩ Y3. (Y ∩̅Z) ∩ X4. (X ∩ Z) - (X ∪ Y)5. Z̅ – (Y ∩ X)The factorial function f(n) = n! is defined by n! = 1 2 3... n whenever n is a positive integer, and O! = 1. Provide big-O estimates for the factorial function and the logarithm of the factorial function. As an illustration, 1! = 1, 2! = 1 2=2, 3! = 1 23 = 6, and 4! = 1 234=24.Take note of how quickly the function n! expands. Consider the following: 20! = 2,432,902,008,176,640,000.
- (Practice) Although the total number of bytes varies from computer to computer, memory sizes of millions and billions of bytes are common. In computer language, the letter M representsthe number 1,048,576, which is 2 raised to the 20th power, and G represents 1,073,741,824, which is 2 raised to the 30th power. Therefore, a memory size of 4 MB is really 4 times 1,048,576 (4,194,304 bytes), and a memory size of 2 GB is really 2 times 1,073,741,824 (2,147,483,648 bytes). Using this information, calculate the actual number of bytes in the following: a. A memory containing 512 MB b. A memory consisting of 512 MB words, where each word consists of 2 bytes c. A memory consisting of 512 MB words, where each word consists of 4 bytes d. A thumb drive that specifies 2 GB e. A disk that specifies 4 GB f. A disk that specifies 8 GBLet A = {c, n, b}, B = {x, y} and C = {0, 1}. Find A)A X B X C B)C X B X A C)B X C X CQuestion 1. Consider bit strings with length land weight k (so strings of l O's and l's, including k l's). We know how to count the number of these for a fixed l and Now, we will count the number of strings for which the sum of the length and the weight is fixed. For example, let's count all the bit strings for which l + k = 11 Find examples of these strings of diffe ent What ·s the longest string possible? What is the shortest? How .many strings are there of each of these Use this to count the total number of strmgs (with sum 11). The other approach: Let n = l + k How many strings have sum n = l? How many have sum n = 2? And so on. Find and explain a recurrence relation for the sequence (an) which gives the number of strmgs with sum n. Describe what you have found abo e in terms of Pascal's What pattern have you discover,ed?
- Consider the following code: for ( i = 0; i < 20; i++) for (j = 0; j < 10; j++) a[i] = a[i] * j a. Give one example of the spatial locality in the code. b. Give one example of the temporal locality in the code.Compute the following values: a) P(5,1) b) P(5,2)c) P(7,3) d) P(5,5) e) P(6,0)f) P(100,2)Recall that histograms are used for constructing load-balanced range partitions. Suppose you have a histogram where values are between 1 and 100, and are partitioned into 10 ranges, 1–10, 11–20,...,91–100, with frequencies 15, 5, 20, 10, 10, 5, 5, 20, 5, and 5, respectively. Give a load-balanced range partitioning function to divide the values into 5 partitions. Write an algorithm for computing a balanced range partition with p partitions, given a histogram of frequency distributions containing n ranges.