From 101ad7e17777a646dc74cc88c335eecb9b21f431 Mon Sep 17 00:00:00 2001
From: newt! <newtykins@outlook.com>
Date: Thu, 26 Aug 2021 01:11:44 +0100
Subject: [PATCH] Add the karatsuba algorithm

---
 python/calculators/karatsuba algorithm.py     | 45 +++++++++++++++++++
 .../ngrams/comparison/comparison.py           | 17 +++----
 readme.md                                     |  1 +
 3 files changed, 55 insertions(+), 8 deletions(-)
 create mode 100644 python/calculators/karatsuba algorithm.py

diff --git a/python/calculators/karatsuba algorithm.py b/python/calculators/karatsuba algorithm.py
new file mode 100644
index 0000000..f80dd88
--- /dev/null
+++ b/python/calculators/karatsuba algorithm.py	
@@ -0,0 +1,45 @@
+def karatsuba(x, y):
+	xLen = len(str(x))
+	yLen = len(str(y))
+	# handle single digit multiplication at the end of the iteration
+	# this gives the loop an end, and gives us our final results
+	if xLen == 1 or yLen == 1:
+		return x * y
+	else:
+		n = max(xLen, yLen) // 2 # choose the longest length
+		# calculate a, b, c, d for the iteration
+		a = x // (10 ** n)
+		b = x % (10 ** n)
+		c = y // (10 ** n)
+		d = y % (10 ** n)
+		# run karatsuba to resolve ac and bd for the iteration
+		ac = karatsuba(a, c)
+		bd = karatsuba(b, d)
+		# use karatsuba again to resolve adbc for the iteration
+		adbc = karatsuba(a + b, c + d) - ac - bd
+		# return the solution for the digit pairs of the iteration
+		return ac * 10 ** (2 * n) + (adbc * 10 ** n) + bd
+
+# helper method to easily take in our inputs
+def takeInput(text):
+	while True:
+		try:
+			x = int(input(text))
+			return x
+		except ValueError:
+			print('You must input an integer!\n')
+
+num1 = takeInput('Please enter a number (:\n')
+num2 = takeInput('Please enter a number to multiply it by!\n')
+
+# Calculate the result and check if it is right
+res = num1 * num2
+karatsubaRes = karatsuba(num1, num2)
+
+print()
+print('Quadratic Result: ', res)
+print('Karatsuba Result: ', karatsubaRes)
+
+if res == karatsubaRes:
+	print()
+	print('The algorithm worked (:')
diff --git a/python/data science/ngrams/comparison/comparison.py b/python/data science/ngrams/comparison/comparison.py
index 7785a1d..daef1fc 100644
--- a/python/data science/ngrams/comparison/comparison.py	
+++ b/python/data science/ngrams/comparison/comparison.py	
@@ -21,17 +21,18 @@ frames = []
 
 for x in data:
 	frame = {}
+	points = x['timeseries']
 	frame['word'] = x['ngram']
-	frame['stdev'] = numpy.std(x['timeseries'])
-	frame['mean'] = numpy.mean(x['timeseries'])
-	frame['median'] = numpy.median(x['timeseries'])
-	frame['mode'] = statistics.mode(x['timeseries'])
-	frame['range'] = max(x['timeseries']) - min(x['timeseries'])
-	frame['q1'] = numpy.percentile(x['timeseries'], 25)
-	frame['q3'] = numpy.percentile(x['timeseries'], 75)
+	frame['stdev'] = numpy.std(points)
+	frame['mean'] = numpy.mean(points)
+	frame['median'] = numpy.median(points)
+	frame['mode'] = statistics.mode(points)
+	frame['range'] = max(points) - min(points)
+	frame['q1'] = numpy.percentile(points, 25)
+	frame['q3'] = numpy.percentile(points, 75)
 	frame['iqr'] = frame['q3'] - frame['q1']
 	frames.append(frame)
-	plt.plot(years, x['timeseries'], label=frame['word'])
+	plt.plot(years, points, label=frame['word'])
 
 df = pandas.DataFrame(frames)
 print(df)
diff --git a/readme.md b/readme.md
index 2526075..06cd797 100644
--- a/readme.md
+++ b/readme.md
@@ -17,6 +17,7 @@
     - [Popularity](python/data%20science/ngrams/popularity/popularity.py)
 - [Calculators](python/calculators)
   - [Binomial Distribution](python/calculators/binomial%20distribution.py)
+  - [Karatsuba Algorithm](python/calculators/karatsuba%20algorithm.py)
   - [Pearson's Product-Moment Correlation Coefficient](python/calculators/pmcc.py)
   - [Quadratic nth Term](python/calculators/quadratic%20nth%20term.py)
   - [Square Root](python/calculators/sqrt.py)