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# ---------------------------------------------------------------
# Imports
# ---------------------------------------------------------------
import time
import matplotlib.pyplot as plt
import scipy as sp
# ---------------------------------------------------------------
# Interface - Timing function
# ---------------------------------------------------------------
def time_them(k, m, *functions):
"""Times the functions (accepting one argument - n) on k values of n up to m
Stops the timing once the function's execution takes:
- more then 2 sec
- more then 1 sec longer then on previous value of n
"""
n_values = list(range(1, m))
if m > k:
n_values = list(range(1, m, m//k))
results = []
for i in range(len(functions)):
print("Testing function " + functions[i].__name__)
results_for_f = []
for n in n_values:
print("\tInput size " + str(n))
before = time.time()
functions[i](n)
after = time.time()
results_for_f.append(after - before)
if results_for_f[-1] > 2 or (len(results_for_f) > 1 and results_for_f[-1] - results_for_f[-2] > 1):
break
results.append(results_for_f)
for i in range(len(functions)):
plt.plot(n_values[:len(results[i])], results[i], label=functions[i].__name__)
plt.legend()
plt.show()
# ---------------------------------------------------------------
# Interface - try out
# ---------------------------------------------------------------
def n_sqrt_n(n):
res = 0
for i in range(n*int(sp.sqrt(n))):
res += 1
return res
def n_squared(n):
res = 0
for i in range(n*n):
res += 1
return res
# ---------------------------------------------------------------
# Interface - Sum to
# ---------------------------------------------------------------
def sum_builtin(n):
"""Sums numbers up to n using built-in function - O(n)"""
print(sum(range(n)))
def sum_explicit(n):
"""Sums numbers up to n explicitely - O(n)"""
total = 0
for i in range(n):
total += i
print(total)
def sum_analytic(n):
"""Sums numbers up to n, analytically - O(1)"""
print(n*(n + 1)//2)
# ---------------------------------------------------------------
# Fibonnachi numbers
# ---------------------------------------------------------------
def fib_n_naive(n):
"""Naive (recursive) way to compute Fibonacci's numbers. O(F(n))"""
if n == 0:
return 0
if n == 1:
return 1
return fib_n_naive(n - 1) + fib_n_naive(n - 2)
def fib_n_efficient(n):
"""Efficient way to compute Fibonacci's numbers. Complexity = O(n)"""
a = 0
b = 1
for i in range(n - 1):
c = a + b
a = b
b = c
print(b)
return b
def fib_n_closed(n):
"""Closed-form computation Fibonacci's numbers. Complexity = O(n)
WRONG! Problems with precision!
"""
fi = (1 + sp.sqrt(5))/2
res = int(round((fi**n - (-fi)**(-n))/sp.sqrt(5)))
print(res)
return res
# ---------------------------------------------------------------
# Sorting
# ---------------------------------------------------------------
BOUND = 1000
# BOUND = 1000000 # try this bound - the linear sort will much more slow down
def sort_selection(n):
"""Sort n random numbers - using inefficient quadratic sort - O(n^2)"""
l = list(sp.random.random_integers(0, BOUND, n))
for i in range(n):
for j in range(i + 1, n):
if l[i] > l[j]:
tmp = l[i]
l[i] = l[j]
l[j] = tmp
def sort_inbuilt(n):
"""Sorts n random numbers - using efficient inbuilt function - O(n log n)"""
l = list(sp.random.random_integers(0, BOUND, n))
l.sort()
def sort_linear(n):
"""Sorts n random numbers bounded in a small range - using efficient linear sort, called Counting sort - O(n)"""
l = list(sp.random.random_integers(0, BOUND, n))
counts = [0]*(BOUND + 1)
for i in l:
counts[i] += 1
counter = 0
for i in range(len(counts)):
for j in range(counts[i]):
l[counter] = i
counter += 1
# ---------------------------------------------------------------
# Main
# ---------------------------------------------------------------
def main():
# time_them(20, 1000, n_sqrt_n, n_squared)
# time_them(20, 1000000, sum_builtin, sum_explicit, sum_analytic)
# time_them(20, 100, fib_n_naive, fib_n_closed, fib_n_efficient)
# time_them(20, 1000, fib_n_closed, fib_n_efficient)
# time_them(20, 10000, sort_inbuilt, sort_linear, sort_selection)
time_them(20, 1000000, sort_inbuilt, sort_linear)
if __name__ == '__main__':
main()
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