Select the asymptotic worst-case time complexity of the following algorithm: Algorithm Input: a1, a2, ., an, a sequence of numbers n, the length of the sequence X, a number Output: ?? For i 1 to n-1 For j i+1 to n If (la; - ajl > 0) Return( "True") End-for End-for Return( "False") O(1) e(n) O eln?) O e(n)

Computer Algorithms Obtain the complexity of the program fragment below   for i <-- 1 to n do k <-- n while K > 1 do K <-- k/2 while (k) end-while end-for

Give the exact number of additions performed in the following segment of certain algorithm assuming a₁, a2, ..., an are positive real numbers and n = 20. for i=1 to n for j=1 to n Sij = ai + aj + 2;

Consider the following recursive algorithm, where // denotes integer division: 3//2 = 1, 5//2 = 2, etc. F(n):if n <= 1:    returnF(n//2)for i from 0 to n    for j from 0 to n//2        print(i+j)    Let function T(n) denote the running time of this algorithm. Derive T(n) and prove its worst case timecomplexity