generate functionSun, 05 Mar 2023

1. Define f(a, b, c, m, i) = Floor[(a*i^2+b*i+c)/m]. 2. define a function T to find S = Sum[f(a, b, c, m, i), {i, 1, n}]. 3. define the values of a, b, c, and m randomly as positive integers less than or equal to 10. 4. for n=10^j with j=1, if the running time of T exceeds log(n) for function T with natural number n, derive an algorithm whose running time does not exceed log(n) for n=10^j, and define a new function U that optimizes function T using this algorithm. 5. compute and output S using U.

#1 def f(a,b,c,m,i): return floor((a*i**2+b*i+c)/m) #2 def T(a,b,c,m,n): S = 0 for i in range(1, n+1): S += f(a,b,c,m,i) return S #3 a = randint(1, 10) b = randint(1, 10) c = randint(1, 10) m = randint(1, 10) #4 T(a,b,c,m,1) #5 U(a,b,c,m,1)

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