Question

我们有一个大的数字，例如（10 ** 1500000）+1，并且想要将其转换为基数3。以下是使用我们在普通Python中发现的最快方法（不使用numpy或CAS库）运行代码。

如何加速基本转换（至基本3）的性能？

我们想知道如何通过以下两种方式做到这一点：

仅使用Python 3的内置函数（没有numpy）吗？
在普通的Python 3程序中使用numpy（或其他CAS库）吗？

非常欢迎任何帮助。这是我们当前的代码：

#### --- Convert a huge integer to base 3 --- ####

# Convert decimal number n to a sequence of list elements
# with integer values in the range 0 to base-1.
# With divmod, it's ca. 1/3 faster than using n%b and then n//=b.
def numberToBase(n, b):
    digits = []
    while n:
        n, rem = divmod(n, b)
        digits.append(rem)
    return digits[::-1]

# Step 2: Convert given integer to another base
# With convsteps == 3, it's about 50-100 times faster than
# with with convsteps == 1, where numberToBase() is called only once.
def step2(n, b, convsteps):
    nList = []
    if convsteps == 3:  # Here the conversion is done in 3 steps
        expos = 10000, 300
        base_a = b ** expos[0]
        base_b = b ** expos[1]
        nList1 = numberToBase(n, base_a)  # time killer in this part
        nList2 = [numberToBase(ll, base_b) for ll in nList1]
        nList3 = [numberToBase(mm, b) for ll in nList2 for mm in ll]
        nList = [mm for ll in nList3 for mm in ll]
    else: # Do conversion in one bulk
        nList = numberToBase(n, b)  # that's the time killer in this part
    return nList


if __name__ == '__main__':

    int_value = (10**1500000)+1  # sample huge numbers
                          # expected begin: [2, 2, 0, 1, 1, 1, 1, 0, 2, 0]
                          # expected time: 4 min with convsteps=3
    base = 3

    # Convert int_value to list of numbers of given base
    # -- two variants of step2() using different convsteps params
    numList = step2(int_value, base, convsteps=1)
    print('   3-1: numList begin:', numList[:10])

    # A value of '3' for the parameter "convsteps" makes
    # step2() much faster than a value of '1'
    numList = step2(int_value, base, convsteps=3)
    print('   3-3: numList begin:', numList[:10])

在How to calculate as quick as possible the base 3 value of an integer which is given as a huge sequence of decimal digits (more than one million)?中在进行基本转换之前，还有一个类似的问题，需要更多步骤。在此问题中，我们将重点放在那部分上，该部分到目前为止大部分时间都在消耗，而对于这一点我们还没有得到答案。

在Convert a base 10 number to a base 3 number中，巨大数字的性能方面也未得到处理。

Answer 1

这是一种方法，该方法通过每次调用的基数平方递归来扩展您的onEvent: function(dt) { $.each(dt.lst, function(ind, ele) { var htm = '<option value="' + ele + '">' + ele + '</option>'; $('#myMultiSelectId').append(htm); }); $('#myMultiSelectId').multiselect({ maxHeight: 300, includeResetOption: true, resetText: 'Deselect All' }); $('#myMultiSelectId').multiselect('rebuild'); }解决方案。需要一些额外的工作才能删除前导零。

convsteps

我的快速计时测试表明，它与您的def number_to_base(n, b): if n < b: return [n] else: digits = [d for x in number_to_base(n, b*b) for d in divmod(x, b)] return digits if digits[0] else digits[1:]在误差范围内相同。但这更简单，并且可能有更少的错误。

使用Python 3快速计算实巨大整数的基数3值

1 个答案: