Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter A.2, Problem 1E
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- Find f(n) and big Oarrow_forwardFind the relation between the following functions: f(n) = log n and g(n) = Vn. (Square root for n)Hint: you may use L'Hopital's Theorem. For function f(n)=log n and time t=1 second, determine the largest size n of a problem that can be solved in time t, assume that the algorithm to solve the problem takes f(n) microseconds. Suppose you have algorithms with the two running times listed below. Suppose you have a computer that can perform 6 operations per second, and you need to compute a result in at most an hour of computation. For each of the algorithms, what is the largest input size n for which you would be able toget the result within an hour for:a) n^3b)10n^2arrow_forwardProve by CASES:Let x be an integer. If 3 does not divide x, then 3 divides x2−1.arrow_forward
- Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X Barrow_forwardsuppose a computer solves a 100x100 matrix using Gauss elimination with partial pivoting in 1 second, how long will it take to solve a 300x300 matrix using Gauss elimination with partial pivoting on the same computer? and if you have a limit of 100 seconds to solve a matrix of size (N x N) using Gauss elimination with partial pivoting, what is the largest N can you do? show all the steps of the solutionarrow_forwardGive the solution for T(n) in the following recurrence. Assume that T(n) is constant for small n. Provide brief justification for the answer.arrow_forward
- Let f (n) and g(n) be positive functions (for any n they give positive values) and f (n) = O(g(n)).Prove or disprove the following statement:arrow_forward6. Let f(n) and g(n) be non-negative functions. Show that: max(f(n), g(n)) = 0(f(n) + g(n)).arrow_forwardFind all solutions for the following pair of simultaneous congruences. 5x = 9 (mod 11) 3x = 8 (mod 13)arrow_forward
- Wilson's Theorem states that for any natural number n >1, n is prime if and only if (n – 1)! = -1 (mod n) Write a function wilson (n) that accepts a natural number n, and returns the remainder of (n – 1)! +1 after division by n. Note: you cannot use numpy here.arrow_forwardGenerate the graph of f(xk) vs k where k is the iteration number and xk is the current estimate of x at iteration k. This graph should convey the decreasing nature of function values.arrow_forward01, Solve the recumence equtions T(n)-T(n- 1) tn Tarrow_forward
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