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92 changes: 67 additions & 25 deletions lib/recursive-methods.rb
Original file line number Diff line number Diff line change
@@ -1,49 +1,91 @@
# Authoring recursive algorithms. Add comments including time and space complexity for each method.

# Time complexity: ?
# Space complexity: ?
# Time complexity: O(n) where n is the value of the input
# Space complexity: O(1) because there's nothing storing the result
def factorial(n)
raise NotImplementedError, "Method not implemented"
return 1 if n == 0
return 1 if n == 1
raise ArgumentError if n < 0
return n * factorial(n - 1)
end

# Time complexity: ?
# Space complexity: ?
# Time complexity: O(n) where n is the length of s
# Space complexity: O(n) where n is the length of s
def reverse(s)
raise NotImplementedError, "Method not implemented"
return s if s.length == 0
last = s[-1]
s = s[0..-2]

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This creates a new string which increases the time and space time complexity.

So the time and space complexity is O(n^2).

reversed_string = last + reverse(s)
return reversed_string
end

# Time complexity: ?
# Space complexity: ?
# Time complexity: O(n) where n is the length of the string
# Space complexity: O(1)

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Space complexity will be O(n) since you end up using the system stack.

def reverse_inplace(s)
raise NotImplementedError, "Method not implemented"
return s if s.length == 0
return s if s.length == 1

reverse_helper(s, 0, s.length - 1)
return s
end

# Time complexity: ?
# Space complexity: ?
def reverse_helper(s, first_index, last_index)

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👍

return if first_index > last_index

temp = s[first_index]
s[first_index] = s[last_index]
s[last_index] = temp
reverse_helper(s, first_index + 1, last_index - 1)
end

# Time complexity: O(n) where n is the value of the input
# Space complexity: O(1)
def bunny(n)
raise NotImplementedError, "Method not implemented"
return 0 if n == 0
return 2 if n == 1
return 2 + bunny(n - 1)
end

# Time complexity: ?
# Space complexity: ?
# Time complexity: O(n) where n is the length of s
# Space complexity: O(1)
def nested(s)
raise NotImplementedError, "Method not implemented"
return true if s == ""
return false if !s.include?("(")

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This isn't a good idea since it goes through the entire length of the string. That means your algorithm is O(n^2).

Instead just check the 1st and last character.

return false if !s.include?(")")
s.sub!("(", "")
s.sub!(")", "")
return nested(s)
end

# Time complexity: ?
# Space complexity: ?
# Time complexity: O(n) where n is the length of the array

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👍

# Space complexity: O(1) because only the variable last storing one element of the array
def search(array, value)
raise NotImplementedError, "Method not implemented"
return false if array.empty?
return true if array[0] == value
last = array.pop
return true if last == value
return search(array, value)
end

# Time complexity: ?
# Space complexity: ?
# Time complexity: O(n) where is the length of s
# Space complexity: O(1) because there's no variable storing the string
def is_palindrome(s)
raise NotImplementedError, "Method not implemented"
return true if s.empty?
if s[0] == s[-1]
s.sub!(s[0], "")

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sub is an O(n) algorithm, so this is an O(n) operation you are doing n times so the full algorithm is O(n^2) for both time and space complexity.

Instead think about tracking the left and right indexes adjusting them each recursive call.

if s.length >= 1
s.sub!(s[-1], "")
end
is_palindrome(s)
else
return false
end
end

# Time complexity: ?
# Space complexity: ?
# Time complexity: O(n) where n is the lenght of the smaller number
# Space complexity: O(1) because there's no variable storing the values of the numbers
def digit_match(n, m)

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👍

raise NotImplementedError, "Method not implemented"
end
return 0 if n == 0 || m == 0
return 1 + digit_match(n / 10, m / 10) if n % 10 == m % 10
return digit_match(n / 10, m / 10)
end
82 changes: 40 additions & 42 deletions specs/recursion_writing_spec.rb
Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
require 'minitest/autorun'
require 'minitest/reporters'
require "minitest/autorun"
require "minitest/reporters"
require "minitest/skip_dsl"
require_relative '../lib/recursive-methods'
require_relative "../lib/recursive-methods"

describe "factorial" do
it "will find the factorial of 0" do
Expand All @@ -23,8 +23,7 @@
answer = factorial(num)

# Assert
expect(answer).must_equal 5*4*3*2*1

expect(answer).must_equal 5 * 4 * 3 * 2 * 1
end

it "will raise an ArgumentError if given a number not >= 0" do
Expand All @@ -38,7 +37,7 @@
end
end

xdescribe "reverse" do
describe "reverse" do
it "will reverse 'cat'" do
# Arrange
string = "cat"
Expand Down Expand Up @@ -83,8 +82,7 @@
end
end


xdescribe "reverse_in_place" do
describe "reverse_in_place" do
it "will reverse 'cat'" do
# Arrange
string = "cat"
Expand Down Expand Up @@ -129,7 +127,7 @@
end
end

xdescribe "bunny" do
describe "bunny" do
it "returns 0 for 0 bunnies" do
# Arrange
count = 0
Expand Down Expand Up @@ -164,7 +162,7 @@
end
end

xdescribe "nested" do
describe "nested" do
it "will return true for empystring" do
# Arrange
string = ""
Expand Down Expand Up @@ -210,7 +208,7 @@
end
end

xdescribe "search" do
describe "search" do
it "will return false for empty array" do
# Arrange
item = "a"
Expand All @@ -224,43 +222,43 @@
end

it "will return true when looking for something in the array" do
# Arrange
item = "a"
array = ["b", "c", "a"]
# Arrange
item = "a"
array = ["b", "c", "a"]

# Act
answer = search(array, item)
# Act
answer = search(array, item)

# Assert
expect(answer).must_equal true
# Assert
expect(answer).must_equal true
end

it "will return false when looking for something not in the array" do
# Arrange
item = "x"
array = ["b", "c", "a"]

# Act
answer = search(array, item)

# Assert
expect(answer).must_equal false
end

it "will return true when finding something at the front of the array" do
# Arrange
item = "b"
array = ["b", "c", "a"]
# Act
answer = search(array, item)
# Assert
expect(answer).must_equal true
end
end

it "will return true when finding something at the front of the array" do
# Arrange
item = "b"
array = ["b", "c", "a"]

# Act
answer = search(array, item)

# Assert
expect(answer).must_equal true
end
end

xdescribe "is_palindrome" do
describe "is_palindrome" do
it "will return true for emptystring" do
# Arrange
string = ""
Expand Down Expand Up @@ -295,7 +293,7 @@
end
end

xdescribe "digit_match" do
describe "digit_match" do
it "returns 4 for 1072503891 and 62530841" do
# Arrange
num1 = 1072503891
Expand All @@ -304,8 +302,8 @@
# Act
answer = digit_match(num1, num2)

# Assert
expect(answer).must_equal 4
# Assert
expect(answer).must_equal 4
end

it "returns 0 for nonmatching numbers" do
Expand All @@ -316,8 +314,8 @@
# Act
answer = digit_match(num1, num2)

# Assert
expect(answer).must_equal 0
# Assert
expect(answer).must_equal 0
end

it "returns 3 for 841 and 62530841" do
Expand All @@ -328,7 +326,7 @@
# Act
answer = digit_match(num1, num2)

# Assert
expect(answer).must_equal 3
# Assert
expect(answer).must_equal 3
end
end
end