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.
import random def f(a, b, c, m, i): return (a*i**2+b*i+c)/m 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 def U(n): a = random.randint(1, 10) b = random.randint(1, 10) c = random.randint(1, 10) m = random.randint(1, 10) return T(a, b, c, m, n) print(U(1000))