How to convert a list of multiple integers into a single integer?

Question

How do I convert a list in Python 3.5 such as:

x=[1, 3, 5]

to an int of 135 (a whole int)?

Answer 1

Using only math (no conversions to or from strings), you can use the reduce function (functools.reduce in Python 3)

b = reduce(lambda total, d: 10*total + d, x, 0)

This makes use of Horner's rule, which factors the polynomial representing the number to reduce the number of multiplications. For example,

1357 = 1*10*10*10 + 3*10*10 + 5*10 + 7     # 6 multiplications
     = ((1*10 + 3)*10 + 5)*10 + 7          # 3 multiplications

As a result, this is faster than computing powers of 10 or creating a string and converting the result to an integer.

>>> timeit.timeit('reduce(lambda t,d: 10*t+d, x, 0)', 'from functools import reduce; x=[1,3,5,7]')
0.7217515400843695
>>> timeit.timeit('int("".join(map(str, [1,3,5,7])))')
1.425914661027491
>>> timeit.timeit('sum(d * 10**i for i, d in enumerate(x[::-1]))', 'x=[1,3,5,7]')
1.897974518011324

---

In fairness, string conversion is faster once the number of digits gets larger.

>>> import timeit

# 30 digits
>>> setup='from functools import reduce; x=[5, 2, 6, 8, 4, 6, 6, 4, 8, 0, 3, 1, 7, 6, 8, 2, 9, 9, 9, 5, 4, 5, 5, 4, 3, 6, 9, 2, 2, 1]' 
>>> print(timeit.timeit('reduce(lambda t,d: 10*t+d, x, 0)', setup))
6.520374411018565
>>> print(timeit.timeit('int("".join(map(str, x)))', setup))
6.797425839002244
>>> print(timeit.timeit('sum(d * 10**i for i, d in enumerate(x[::-1]))', setup))
19.430233853985555

# 60 digits
>>> setup='from functools import reduce; x=2*[5, 2, 6, 8, 4, 6, 6, 4, 8, 0, 3, 1, 7, 6, 8, 2, 9, 9, 9, 5, 4, 5, 5, 4, 3, 6, 9, 2, 2, 1]' 
>>> print(timeit.timeit('reduce(lambda t,d: 10*t+d, x, 0)', setup))
13.648188541992567
>>> print(timeit.timeit('int("".join(map(str, x)))', setup))
12.864593736943789
>>> print(timeit.timeit('sum(d * 10**i for i, d in enumerate(x[::-1]))', setup))
44.141602706047706

# 120 digits!
>>> setup='from functools import reduce; x=4*[5, 2, 6, 8, 4, 6, 6, 4, 8, 0, 3, 1, 7, 6, 8, 2, 9, 9, 9, 5, 4, 5, 5, 4, 3, 6, 9, 2, 2, 1]' 
>>> print(timeit.timeit('reduce(lambda t,d: 10*t+d, x, 0)', setup))
28.364255172084086
>>> print(timeit.timeit('int("".join(map(str, x)))', setup))
25.184791765059344
>>> print(timeit.timeit('sum(d * 10**i for i, d in enumerate(x[::-1]))', setup))
99.88558598596137