Add karatsuba algorithm

[appleJax]

This PR adds the Karatsuba fast multiplication algorithm to the algorithms/math folder.

README.md

Karatsuba Multiplication

Karatsuba is a fast multiplication algorithm discovered by Anatoly Karatsuba in 1960. Given two n-digit numbers, the "grade-school" method of long multiplication has a time complexity of O(n²), whereas the karatsuba algorithm has a time complexity of O(n^1.59).

Recursive Formula

x = 1234
y = 5678

karatsuba(x, y)

1. Split each number into numbers with half as many digits

a = 12
b = 34

c = 56
d = 78

2. Compute 3 subexpressions from the smaller numbers

• ac = a * c
• bd = b * d
• abcd = (a + b) * (c + d)

3. Combine subexpressions to calculate the product

A = ac * 10000
B = (abcd - ac - bd) * 100
C = bd

x * y = A + B + C

Note: The karatsuba algorithm can be applied recursively to calculate each product in the subexpressions. (a * c = karatsuba(a, c)). When the numbers get smaller than some arbitrary threshold, they are multiplied in the traditional way.

References

Stanford Algorithms (YouTube)
Wikipedia

[codecov]

Codecov Report

Merging #225 into master will not change coverage.
The diff coverage is 100%.

@@          Coverage Diff          @@
##           master   #225   +/-   ##
=====================================
  Coverage     100%   100%           
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  Files         143    144    +1     
  Lines        2554   2569   +15     
  Branches      422    423    +1     
=====================================
+ Hits         2554   2569   +15

Impacted Files	Coverage Δ
...orithms/math/karatsuba-multiplication/karatsuba.js	100% <100%> (ø)

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