Add small Python recursion exercises

recursion-exercises.py

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+# function to sum integers via recursion
+def total(numbers):
+	# if recursion not needed due to too few items
+	if len(numbers) == 1:
+		return numbers[0]
+	return numbers[0] + total(numbers[1:])
+
+# function to find if number is prime via recursion
+def prime(number, divisor = None):
+	# create initial divisor, only if it doesn't exist
+	if not divisor:
+		# divide by two because all factors are duplicated - searching through all numbers smaller than the given number would search all factor pairs twice
+		# floor divide because if it's not an integer, it's not a valid factor - so can be ignored
+		# if rounded up, the number's compliment will appear again later, in the reverse of the factor pair
+		divisor = number // 2
+	# number isn't a prime if less than two, or if it has a factor that's greater than one
+	if (number <= 1) or (divisor > 1 and number % divisor == 0):
+		return False
+	# all prime have been checked, and none are factors of the number
+	elif (divisor <= 1):
+		return True
+	else:
+		return prime(number, divisor - 1)
+
+# function for binary search via recursion
+def search(item, list):
+	# get middle index (-1 accounts for zero-based indexing)
+	midpoint = (len(list) + 1) // 2 - 1
+	# item found
+	if item == list[midpoint]:
+		return True
+	# all of list searched and item not found
+	elif (len(list) == 1):
+		return False
+	# item is larger than the middle item, so must be in the larger half of the list
+	elif item > list[midpoint]:
+		return search(item, list[midpoint + 1:])
+	# item is smaller than the middle item, so must be in the smaller half of the list
+	else:
+		return search(item, list[:midpoint])