Let A(n) = 8 A(n/2)+ n³ the time of this recurrence equation is Select one: O a. O(n*) O b.O (2") c. O(n³) O d. O(n³ logn)
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- Show that log(n!) = O(n log(n))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)Given f(n) ∈ Θ(n), prove that f(n) ∈ O(n²). Given f(n) ∈ O(n) and g(n) ∈ O(n²), prove that f(n)g(n) ∈ O(n³).
- What are the complexities of the following code segments in terms of n? Give an upper bound. a) int i=1;while (i<= n) { int j = i; while (j > 0) j = j/2;i++; } b) int i,j s=0; for (i=0; i<n; i++) { i--; s++; if (s == n) { i++; s = 0; } } c) while (n > 0) { for (int i=0; i<n; i++) sum++; n = n/2; }Give a Θ(lg n) algorithm that computes the remainder when xn is divided byp. For simplicity, you may assume that n is a power of 2. That is, n = 2k forsome positive integer k.nput a integer n from us’e‘(;i srint value of 2*n*log(n). guage -
- RSA How do you find a ‘p’ and ‘q’ given a number n and φ(n)? Using x^2 - [n-φ(n)+1]x+n = 0 to find p and q. p and q are relatively prime. n=pq Φ(n) = (p-1)(q-1) Give an Example.Assume that for any integer n is greater than or equal to one prove or disprove the following a)n^2 − n + 1 is O(n) b)5^n is O(4^n) c) n(log(n))^4 is O(n^4/3)Generate random matrices of size n × n where n = 100, 200, . . . , 1000. Also generate a random b ∈ R n for each case. Each number must be of the form m.dddd (Example : 4.5444) which means it has 5 Significant digits in total