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Puzzle: Last digit of a large number [algorithms]

Last digit of a large number” is a coding puzzle that people can be attempted in the following languages: haskell, javascript, python, ruby, kotlin, cpp, r, rust, and purescript.

  • Difficulty: 5 kyu
  • Stars: 535
  • Votes: 910
  • Category: algorithms
  • Tags: Algorithms
  • Source: codewars

Description

Define a function that takes in two non-negative integers $a$ and $b$ and returns the last decimal digit of $a^b$. Note that $a$ and $b$ may be very large!

For example, the last decimal digit of $9^7$ is $9$, since $9^7 = 4782969$. The last decimal digit of $({2^{200}})^{2^{300}}$, which has over $10^{92}$ decimal digits, is $6$. Also, please take $0^0$ to be $1$.

You may assume that the input will always be valid.

Examples

haskell
lastDigit 4 1             `shouldBe` 4
lastDigit 4 2             `shouldBe` 6
lastDigit 9 7             `shouldBe` 9
lastDigit 10 (10^10)      `shouldBe` 0
lastDigit (2^200) (2^300) `shouldBe` 6

javascript
lastDigit("4", "1")            // returns 4
lastDigit("4", "2")            // returns 6
lastDigit("9", "7")            // returns 9
lastDigit("10","10000000000")  // returns 0

python
last_digit(4, 1)                # returns 4
last_digit(4, 2)                # returns 6
last_digit(9, 7)                # returns 9
last_digit(10, 10 ** 10)        # returns 0
last_digit(2 ** 200, 2 ** 300)  # returns 6

kotlin
lastDigit(4, 1)                # returns 4
lastDigit(4, 2)                # returns 6
lastDigit(9, 7)                # returns 9
lastDigit(10, 10 ** 10)        # returns 0
lastDigit(2 ** 200, 2 ** 300)  # returns 6

ruby
last_digit(4, 1)                # returns 4
last_digit(4, 2)                # returns 6
last_digit(9, 7)                # returns 9
last_digit(10, 10 ** 10)        # returns 0
last_digit(2 ** 200, 2 ** 300)  # returns 6

cpp
last_digit("4", "1")            // returns 4
last_digit("4", "2")            // returns 6
last_digit("9", "7")            // returns 9
last_digit("10","10000000000")  // returns 0

r
last_digit("4", "1")            # returns 4
last_digit("4", "2")            # returns 6
last_digit("9", "7")            # returns 9
last_digit("10","10000000000")  # returns 0

rust
last_digit("4", "1")            // returns 4
last_digit("4", "2")            // returns 6
last_digit("9", "7")            // returns 9
last_digit("10","10000000000")  // returns 0

purescript
lastDigit "4" "1"            -- => 4
lastDigit "4" "2"            -- => 6
lastDigit "9" "7"            -- => 9
lastDigit "10" "10000000000" -- => 0


Remarks

JavaScript, C++, R, PureScript

Since these languages don’t have native arbitrarily large integers, your arguments are going to be strings representing non-negative integers instead.

Solve It Here

Click the link below to solve it on Codewars:

Notes

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1 Like

I did this one in Python.