Homework Solution: Using the formal definitions of Big-O show that a. n^2 + n + 11 elementof O(n^2) b. n^2 elemento…

    3. Using the formal definitions of Big-O show that a, n^2 + n + 11 E 0(n^2) c. gln) EO(n) 4. Using the definitions of Big-O and Ω and θ a. Show that n3n+ lg(n) E O(n2) b. Show that n2+ 3n +lg(n) E Ω(n2) c. show that n2 + 3n +lg(n) E θ(n*) 5. Using the definitions of Big-O and o a. Show that n E o(n) using a proof by contradiction
    Using the formal definitions of Big-O show that a. n^2 + n + 11 elementof O(n^2) b. n^2 elementof O(n^2+6n) c. lg(n) elementof O(n) Using the definitions of Big-O and Ohm and theta a. Show that n^2 + 3n+ lg(n) elementof Ohm (n^2) c. Show that n^2 + 3n + lg(n) elementof Ohm (n^2) Show that n^2 + 3n+lg(n) elementof theta(n^2) Using the definitions of Big-O and o a. Show that n g o[n) using a proof by contradiction

    Expert Answer

     
    O(g(n)) = { f(n): there exist positive constants c and

    3. Using the explicit definitions of Big-O demonstration that a, n^2 + n + 11 E 0(n^2) c. gln) EO(n) 4. Using the definitions of Big-O and Ω and θ a. Demonstration that n3n+ lg(n) E O(n2) b. Demonstration that n2+ 3n +lg(n) E Ω(n2) c. demonstration that n2 + 3n +lg(n) E θ(n*) 5. Using the definitions of Big-O and o a. Demonstration that n E o(n) using a probation by contradiction

    Using the explicit definitions of Big-O demonstration that a. n^2 + n + 11 elementof O(n^2) b. n^2 elementof O(n^2+6n) c. lg(n) elementof O(n) Using the definitions of Big-O and Ohm and theta a. Demonstration that n^2 + 3n+ lg(n) elementof Ohm (n^2) c. Demonstration that n^2 + 3n + lg(n) elementof Ohm (n^2) Demonstration that n^2 + 3n+lg(n) elementof theta(n^2) Using the definitions of Big-O and o a. Demonstration that n g o[n) using a probation by contradiction

    Expert Counterpart

     

    O(g(n)) = { f(n): there consist dogmatical constants c and 
                      n0 such that 0 <= f(n) <= cg(n) control 
                      integral n >= n0}
    

    3) a) n2+n+11 < 2 n2

    Take c as 2 and n0=4

    0 <= f(n) <= cg(n) control integral n >= n0
    

    =>O(n2) Complexity

    b) n2 <= c n2 + 6n

    Take c=1 and n0=1

    n2 < =n2 + 6n

    =>Complexity O(n2 + 6n)

    c) lg(n) <= c n

    Take c=1 and n0=1

    lg(n) <= n

    =>Complexity O(n)