Consider the following algorithm. for i +[1.2.3.4.5.6} do beep, for j={1,2,3} do beep, for k={1,2,3,4} do beep, for / = {1,2,3,4} do beep, for m = {1,2,3,4,5} do beep. How many times does a beep statement get executed?
Consider the following algorithm. for i +[1.2.3.4.5.6} do beep, for j={1,2,3} do beep, for k={1,2,3,4} do...
(b) Consider the following algorithm for (i = n; i >-1; i i/2) for j in range [1, i] Constant Number of Operations Derive the run time of the above algorithm (as a function of n). You must formally derive the run-times (merely stating run times or high level explanation of run time do not suffice)
Consider the following pseudo-code: // Assume i, j, k are integers for i = 1 to n do for j = n-i+1 to n { k = 1; while (k*k <= j) { perform <op>; k = k + 1; } } Find an expression for f(n), the number of times is performed. Find g(n) so that f(n) is Θ(g(n)). Prove your answer.
Exercise 7.3.5: Worst-case time complexity - mystery algorithm. The algorithm below makes some changes to an input sequence of numbers. MysteryAlgorithm Input: a1, a2....,an n, the length of the sequence. p, a number Output: ?? i != 1 j:=n While (i < j) While (i <j and a < p) i:= i + 1 End-while While (i <j and a 2 p) j:=j-1 End-while If (i < j), swap a, and a End-while Return( aj, a2,...,an) (a) Describe in English...
Algorithm performance Give the order of magnitude Theta () for the following algorithm. Explain why your answer is correct. GET VALUES for A_1, A_2, .. ., A_n, and B_1, B_2, .. ., B_n Get value of n i = 1/* set i equal to 1 */DO WHILE (i lessthanorequalto n)/* for each of the n values in A */j = 1/* set j equal to 1 */DO WHILE (j lessthanorequalto n)/* Do n times *1 IF Ai = Bj THEN...
Explain please
II. (7 points) Consider the following bit of pseudocode: for (int k = 1; ks Ign; k++) (for (int i = 1; i r: i++) Print "Hello World"; for (int j-1;jsn:j++) Print "Hello World" when n = 2, how many times will "Hello World" be printed? When n 4, how many times will "Hello World be printed? O Assuming that the print is the basic operation, what is the complexity function of this pseudocode?
II. (7 points) Consider...
ALGORITHM X(A[0..n - 1]) // Input: A contains n real numbers for it 0 to n - 2 do for jt i +1 to n - 1 do if Aj] > A[i] swap A[i] and A[j] 1. What does this algorithm compute? 2. What is the basic operation? 3. How many times is the basic operation executed? 4. What is the efficiency class of this algorithm?
Consider the following algorithm. ALGORITHM Enigma(A[0.n - 1]) //Input: An array A[0.n - 1] of integer numbers for i leftarrow 0 to n - 2 do for j leftarrow i +1 to n - 1 do if A[i] = = A[j] return false return true a) What does this algorithm do? b) Compute the running time of this algorithm.
(1) Give a formula for SUM{i} [i changes from i=a to i=n], where a is an integer between 1 and n. (2) Suppose Algorithm-1 does f(n) = n**2 + 4n steps in the worst case, and Algorithm-2 does g(n) = 29n + 3 steps in the worst case, for inputs of size n. For what input sizes is Algorithm-1 faster than Algorithm-2 (in the worst case)? (3) Prove or disprove: SUM{i**2} [where i changes from i=1 to i=n] ϵ tetha(n**2)....
(V). Given the following algorithm, answer relevant questions. Algorithm 1 An algorithm 1: procedure WHATISTHIS(21,22,...,n: a list of n integers) for i = 2 to n do c= j=i-1 while (j > 0) do if ra; then break end if 4j+1 = a; j= j-1 end while j+1 = 1 end for 14: return 0.02. 1, 15: end procedure Answer the following questions: (1) Run the algorithm with input (41, 02, 03, 04) = (3, 0, 1,6). Record the values...
Construct a TM that accepts the following language. Write the high-level algorithm executed by the machine and label the sections(5 points). {a^i b^j c^k | i + j = k}