XerY.py

# This Python file uses the following encoding: utf-8

import math

def log(a):
    log_version = 2
    return math.log(a, log_version)

# defining n to some random large number (to compute results)
n = 123

# Compare run-times using asymptotic notation

def c1(x, y):
    # x er O(y)
    print("Case 1: x er O(y)")
    print(str(x)+" er <=("+str(y)+"): " + str(x <= y) + "\n")
    #if (x+y < n and x < 50 and y < 50): # X and Y are MOST LIKELY constants, e.g. "x = 4, y = 3"
    #    print(str(x)+" er <=("+str(y)+"): TRUE, (both constant time)")
    #else: # do original func
    #    print(str(x)+" er <=("+str(y)+"): " + str(x <= y) + "\n")

def c2(x, y):
    # x er Ω(y) --- \u03A9
    print("Case 2: x er Omega(y)")
    print(str(x)+" er >=("+str(y)+"): " + str(x >= y) + "\n")

def c3(x, y):
    # x er ϴ(y) --- \u03F4
    print("Case 3: x er Theta(y)")
    print(str(x)+" er =("+str(y)+"): " + str(x == y) + "\n")

def c4(x, y):
    # x er o(y)
    print("Case 4: x er o(y)")
    print(str(x)+" er <("+str(y)+"): " + str(x < y) + "\n")

def c5(x, y):
    # x er ω(y) --- \u03C9
    print("Case 5: x er w(y)")
    print(str(x)+" er >("+str(y)+"): " + str(x > y) + "\n")

# Noter:
# - "kvadratrod(x)" er "math.sqrt(x)"
# - "n^2" er "n**2"
# - Konstanter "(1,2,3...)" har altid samme voksehastighed! De er altid lavest voksehastighed i forhold til andre!

# OUTPUT:
c1(n**(1/4), n**(1/3)) # x er O(y) --- Konstanter (1,2,3...) er altid = TRUE, (konstant voksehastighed)!
#c2(x, y) # x er Ω(y)
#c3(x, y) # x er ϴ(y)
#c4(x, y) # x er o(y)
#c5(x, y) # x er ω(y)