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 math
import random

def f(a, b, c, m, i):
  return math.floor((a*(i**2) + b*i + c) / m)

def T(n):
  a = random.randint(1, 10)
  b = random.randint(1, 10)
  c = random.randint(1, 10)
  m = random.randint(1, 10)
  S = 0
  for i in range(1, n+1):
    S += f(a, b, c, m, i)
  return S, a, b, c, m

n = 100
S, a, b, c, m = T(n)
print("S =", S)
print("a =", a)
print("b =", b)
print("c =", c)
print("m =", m)