如果我编写两个计算相同内容的软件,但其中一个软件的速度是它的两倍.这是否意味着不同的复杂程度？

Question

对于给定的余额和利率,我的计划计算一年内偿还债务的最低月付款.然而,一个平均计算在~0.000150s,另一个计算在~0.000300s.这是否意味着不同程度的渐近复杂性？

这些是代码示例:

较慢的一个:

import time
start_time = time.time()

balance = 999999
annualInterestRate = 0.18
mRate = annualInterestRate/12
high = (((mRate+1)**12)*balance)/12
low = balance/12
guessed = False

def balanceLeft(balance,mRate,minPayment):
    monthsLeft = 12
    while monthsLeft > 0:
        unpaidBalance =  balance - minPayment
        interest = mRate * unpaidBalance
        balance = unpaidBalance
        balance += interest
        monthsLeft -= 1
    return balance

while guessed == False:
    minPayment = (high + low) / 2
    if round(balanceLeft(balance,mRate,minPayment),2) < 0:
        high = minPayment
    elif round(balanceLeft(balance,mRate,minPayment),2)> 0:
        low = minPayment
    else:
        if abs(round(balanceLeft(balance,mRate,minPayment),2) - 0) < 0.01:
            guessed = True

print('Lowest Payment: ',end='')
print(round(minPayment,2))

print("time elapsed: {:.6f}s".format(time.time() - start_time))

越快越快

import time
start_time = time.time()

annualInterestRate = 0.18
rate = annualInterestRate / 12
monthsLeftr = 12
xCoefficent = 1 + rate
ConstantTerm = 1 + rate
while monthsLeftr > 1:
    xCoefficent = (xCoefficent + 1) * ConstantTerm
    monthsLeftr -= 1


balance = 999999
monthsLeft = 12
while monthsLeft > 0:
    balance = balance * ConstantTerm
    monthsLeft -= 1
minPayment = balance / xCoefficent


print('Lowest Payment: ', end="")
print(round(minPayment,2))

print("time elapsed: {:.6f}s".format(time.time() - start_time))

Answer 1

绝对不.

渐近复杂性从不描述绝对运行时间,而是问题大小增加时的趋势.

实际上,对于小问题实例,具有更好渐近复杂度的算法运行速度更慢.