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 For k=1 to n If ((ai)^2 + (aj)^2 = (ak)^2) Return("True") End-for End-for End-for Return("False") 1) 0(1) 2) 0 (n) 3) 0 (n²) 4) 0(n³)

Give the time complexity for the following algorithm. You need to identify the basic operation first. F(int n) { if (n>1) Return F(n/3)+F(n/3)+5; else return 1; } 1) What is the basic operation? 2) Set up the recurrence. Let T(n) be the # of basic operations 3) Solve the recurrence using the Master theorem

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