Question

我正在解决leetcode的帕斯卡三角问题。我观察到两个for循环分别执行相同的任务，但是使用递减循环解决它给了我一个低效的解决方案。

给定非负索引k，其中k≤33，返回第k个索引行   帕斯卡的三角形。

请注意，行索引从0开始。

增量循环解决方案

class Solution(object):
    def getRow(self, rowIndex):
        """
        :type rowIndex: int
        :rtype: List[int]
        """
        result = [1 for _ in range(rowIndex+1)]

        for i in range(2,rowIndex+1):
            for j in range(1,i):
                result[i-j] = result[i-j]+result[i-j-1]
        return result

减少循环解决方案

class Solution(object):
    def getRow(self, rowIndex):
        """
        :type rowIndex: int
        :rtype: List[int]
        """
        result = [1 for _ in range(rowIndex+1)]

        for i in range(2,rowIndex+1):
            for j in range(i-1,0,-1):
                result[j] = result[j]+result[j-1]
        return result

这是真的吗？

Answer 1

首先，这是一个函数，它返回一行Pascal三角形的列表而不计算前一行。它为整数n >= 0提供了正确的输出。

def pascal(n):
    ''' Row n of Pascal's triangle '''
    p = 1
    row = [p]
    for i in range(1, n+1):
        p = p * n // i
        n -= 1
        row.append(p)
    return row

# test 
for n in range(8):
    print(n, pascal(n))

<强>输出

0 [1]
1 [1, 1]
2 [1, 2, 1]
3 [1, 3, 3, 1]
4 [1, 4, 6, 4, 1]
5 [1, 5, 10, 10, 5, 1]
6 [1, 6, 15, 20, 15, 6, 1]
7 [1, 7, 21, 35, 35, 21, 7, 1]

这里有一些使用标准timeit模块的代码，用于比较各种方法的时间。

from __future__ import print_function
from timeit import Timer

def getRow_inc(rowIndex):
    result = [1] * (rowIndex + 1)
    for i in range(2, rowIndex + 1):
        for j in range(1, i):
            result[i-j] = result[i-j] + result[i-j-1]
    return result

def getRow_dec(rowIndex):
    result = [1] * (rowIndex + 1)
    for i in range(2, rowIndex + 1):
        for j in range(i-1, 0, -1):
            result[j] = result[j] + result[j-1]
    return result

def pascal(n):
    ''' Row n of Pascal's triangle '''
    p = 1
    row = [p]
    for i in range(1, n+1):
        p = p * n // i
        n -= 1
        row.append(p)
    return row

funcs = (getRow_inc, getRow_dec, pascal)

def time_test(size, loops):
    timings = []
    for func in funcs:
        t = Timer(lambda: func(size))
        result = sorted(t.repeat(3, loops))
        timings.append((result, func.__name__))
    timings.sort()
    for result, name in timings:
        print('{0:10} : {1}'.format(name, result))
    print()

def verify(size):
    return getRow_inc(size) == getRow_dec(size) == pascal(size)

loops = 8192
size = 2
for i in range(6):
    print('Size:', size, 'Loops:', loops, verify(size))
    time_test(size, loops)
    size <<= 1
    loops >>= 1

python 2.6输出

Size: 2 Loops: 8192 True
pascal     : [0.043977975845336914, 0.044337987899780273, 0.044638156890869141]
getRow_inc : [0.051661968231201172, 0.051739931106567383, 0.05926203727722168]
getRow_dec : [0.051797866821289062, 0.052932977676391602, 0.053112030029296875]

Size: 4 Loops: 4096 True
pascal     : [0.030641078948974609, 0.031950950622558594, 0.035629987716674805]
getRow_dec : [0.053617000579833984, 0.054769992828369141, 0.056906938552856445]
getRow_inc : [0.058582067489624023, 0.059936046600341797, 0.066784143447875977]

Size: 8 Loops: 2048 True
pascal     : [0.024718999862670898, 0.024795055389404297, 0.024961948394775391]
getRow_dec : [0.071218013763427734, 0.072144031524658203, 0.073839902877807617]
getRow_inc : [0.085191011428833008, 0.085605144500732422, 0.093863964080810547]

Size: 16 Loops: 1024 True
pascal     : [0.021828889846801758, 0.021852970123291016, 0.022058010101318359]
getRow_dec : [0.11763501167297363, 0.12208914756774902, 0.13960886001586914]
getRow_inc : [0.15797996520996094, 0.16045904159545898, 0.1609339714050293]

Size: 32 Loops: 512 True
pascal     : [0.027434110641479492, 0.027448892593383789, 0.027502059936523438]
getRow_dec : [0.21527910232543945, 0.21595311164855957, 0.25867199897766113]
getRow_inc : [0.29518985748291016, 0.30337095260620117, 0.30416202545166016]

Size: 64 Loops: 256 True
pascal     : [0.029985904693603516, 0.030019044876098633, 0.030050039291381836]
getRow_dec : [0.44218015670776367, 0.46946215629577637, 0.49126601219177246]
getRow_inc : [0.63355302810668945, 0.63923096656799316, 0.68472099304199219]

python 3.6输出

Size: 2 Loops: 8192 True
pascal     : [0.04358131700064405, 0.04425547199934954, 0.04470863800088409]
getRow_inc : [0.05114753599991673, 0.051217224998254096, 0.05178851000164286]
getRow_dec : [0.05115222699896549, 0.051395288999628974, 0.05416869800319546]

Size: 4 Loops: 4096 True
getRow_dec : [0.057865087997925, 0.08918459000051371, 0.11932526199962012]
pascal     : [0.05869485400035046, 0.06098903500242159, 0.0629262660004315]
getRow_inc : [0.0613923060009256, 0.06144011699871044, 0.08097989900124958]

Size: 8 Loops: 2048 True
pascal     : [0.023705500996584306, 0.024017232997721294, 0.0252248659999168]
getRow_dec : [0.07945838300292962, 0.07997345200055861, 0.10279535600056988]
getRow_inc : [0.0951986139989458, 0.10361288200147101, 0.12552303700067569]

Size: 16 Loops: 1024 True
pascal     : [0.022952020000957418, 0.022961610000493238, 0.024299886001244886]
getRow_dec : [0.13245858099980978, 0.13321232800080907, 0.13570772599996417]
getRow_inc : [0.17226859199945466, 0.17394291900200187, 0.20096674900196376]

Size: 32 Loops: 512 True
pascal     : [0.023837570999603486, 0.03626328599784756, 0.04858057100136648]
getRow_dec : [0.25379533899831586, 0.25503273499998613, 0.25983839800028363]
getRow_inc : [0.3346854230003373, 0.33851587800018024, 0.37444046800010256]

Size: 64 Loops: 256 True
pascal     : [0.024329154002771247, 0.024376211000344483, 0.025199785999575397]
getRow_dec : [0.5039554230024805, 0.5147428849995777, 0.529499655996915]
getRow_inc : [0.6677602630006731, 0.6715008999999554, 0.6890275240002666]

Python的递减循环是否比递增循环运行得慢？

1 个答案: