A) Find a recurrence relation for an - number of n digit quarternary sequences (using digts from ...
06. Do any two of the following three parts Q6(a). Solve the following recurrence relation; Q6(b). Find a recurrence relation for an, which is the number of n-digit binary sequences with no pair of consecutive 1s. Explain your work. Q6(c) Solve the following problem using the Inclusion-Exclusion formula. How many ways are there to roll 8 distinct dice so that all the six faces appear? Hint: Use N(A'n n. NU)-S-,-1)' )-S-S2+S-(-1)Sn U- All possible rolls of 8 dice, Aj-Roll of...
4 a) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 21 subsequence. b) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 44 subsequence. Answer is a) an = an-1+ an-4 + an-2 - an-3, b) an = an-1 + an-2 + an-5 + an-6, please explain how to get it,...
4 a) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 21 subsequence. b) Find a recurrence relation for an, the number of sequences of 1's and 2's and 4's whose sum is n and with no 44 subsequence. Answer is a) an = an-1+ an-4 + an-2 - an-3, b) an = an-1 + an-2 + an-5 + an-6, please explain how to get it,...
Need answers for 1-5 Consider the following recurrence relation: H(n) = {0 if n lessthanorequalto 0 1 if n = 1 or n = 2 H(n - 1) + H (n - 2)-H(n - 3) if n > 2. (a) Compute H(n) for n = 1, 2, ...., 10. (b) Using the pattern from part (a), guess what H(100) is. 2. Consider the recurrence relation defined in Example 3.3 (FROM TEXT BOOK, also discussed in class and shown in slides)...
1-find the recurrence relation using power series solutions. 2-find the first four terms in each of two solutions y1 and y2 3-by evaluating wronskian w(y1,y2) show that they from a fundamental solution set. Iy yry 0, zo = 1
do (b) please 2. (15 marks) Consider the abstract datatype SEQ whose objects are sequences of elements and which supports two operations . PREPEND(x, S), which inserts element r at the beginning of the sequence S and . ACCESS(S, i), which returns the ith element in the sequence Suppose that we represent S by a singly linked list. Then PREPEND(, S) takes 1 step and ACCESS(S, i) takes i steps, provided S has at least i elements Suppose that S...
Discrete mathematics 2) Let be eumber of ternary strings (of 0s, 1s and 2s) of length n that have no adjacent even digits. For example, so (the empty string), s3 (the strings 0, 1 and 2), while s2 5: 01, 0, 12, 2 because the strings 00,02, 20, 22 are not allowed, as they have adjacent even digits. As another example, the string 10112 is allowed, while the strings 10012 and 120121 are not allowed (a) Find #3; (b) find...
Example from screen cast (a) Write the recurrence relation for Binary Search, using the formula T(n) = aT(n/b) + D(n) + C(n). (We'll assume T(1) = C, where c is some constant, and you can use c to represent other constants as well, since we can choose c to be large enough to work as an upper bound everywhere it is used.) (b) Draw the recursion tree for Binary Search, in the style shown in screencast 2E and in Figure...
r the recurrence relation o. Consider T(n) = Vn T(Vn) + n a. Why can't you solve this with the master theorem? b. S t involves a constant C, tell me what it is in terms of T(O), T(1), or whatever your inequality by induction. Show the base case. Then show the how that T( n)= 0(n lg ig n). First, clearly indicate the inequality that you wish to hen proceed to prove the inductive hypothesis inductive case, and clearly...
If someone can help with 3 3) To multiply 2 n bit binary numbers the straightforward way takes (r) time because each digit of each number multiplies each digit of the other number. (The aditions from carying are lower order terms.) Consider the following divide- and-conquer algorithm, which assumes, for simplicity, that n is a power of 2: Split each number into 2 collections of bits, the high order bits and the low order bits. For convenience, call the two...