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)