Assuming you're only dealing with positive numbers, you can divide each number by the largest power of 10 smaller than the number, and then take the floor of the result.
>>> from math import log10, floor
>>> lst = [34523, 55, 65, 2]
>>> [floor[x / [10**floor[log10[x]]]] for x in lst]
[3, 5, 6, 2]
If you're using Python 3, instead of flooring the result, you can use the integer division operator //:
>>> [x // [10**floor[log10[x]]] for x in lst]
[3, 5, 6, 2]
However, I have no idea whether this is more efficient than just converting to a string and slicing the first character. [Note that you'll need to be a bit more sophisticated if you have to deal with numbers between 0 and 1.]
>>> [int[str[x][0]] for x in lst]
[3, 5, 6, 2]
If this is in a performance-critical piece of code, you should measure the two options and see which is faster. If it's not in a performance-critical piece of code, use whichever one is most readable to you.
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I'm doing a project euler problem [//projecteuler.net/problem=40] that requires iteration of each digit of a set of increasing integers, in order.
I solved it by converting each integer to a string and taking the 0 index, but I'd like to know if there's a better, numerical algorithm to find the most significant digit of an arbitrarily long given integer.
Example: Given 3918287712, to easily get both [3] and find the power of 10 [10^10] that corresponds to it. I'd really like pointers to mathematical literature as well - I'm trying to increase my own knowledge of math and algorithms.
asked Jul 6, 2013 at 16:09
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Arithmetically, the number of digits of a positive integer $N$ is $d=\lfloor \log_{10} N\rfloor + 1$. For example, $\log_{10} 3918287712 \approx 9.5931$, so $3918287712$ has $\lfloor 9.5931\rfloor + 1 = 10$ digits.
Once you know the number of digits $d$ of $N$, you can find the first digit $f$ of $N$ by calculating $f = \lfloor N/10^{d-1} \rfloor$. For example, the first digit of $3918287712$ is $\lfloor 3918287712/10^{10-1} \rfloor = \lfloor 3.918287712 \rfloor = 3$.
[In practice, your string-based method might be faster...!]
answered Jul 6, 2013 at 17:39
Greg MartinGreg Martin
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Given two positive integers X and Y, the task is to find the
MSB of X, in the given base Y.
Examples:
Input: X = 55, Y = 3
Output: 2
Explanation:
55 is 2001 in base 3 with first digit as 2.
Input: X = 123, Y = 10
Output: 1
Explanation:
123 is 123 in base 10 with first digit 1.
Approach: Let the task to find 1st digit of X = 1234 in base Y = 10, So to get First digit = 1:
Divide 1234 by 1000
= X / 103
= X / 10Number of Digits in X – 1
= X / 10log[X] / log[10] [which is for base 10]
For any other base, we can replace 10 with Y. Therefore, we can calculate the first digit of a number X in base Y by using the formula:
X / Y[log[X]/log[Y]]
Below is the implementation of the above approach:
C++
#include
using namespace std;
void first_digit[int x, int y]
{
int length = log[x] / log[y] + 1;
int
first_digit = x / pow[y, length - 1];
cout