Erika - Branches

README.md

@@ -2,6 +2,8 @@
 
 Dynamic programming is a strategy for developing an algorithm where each subproblem is solved and the results recorded for use in solving larger problems.  In this exercise you will write a pair of dynamic programming methods.
 
+**Due March 30th 7pm**
+
 ## Wave 1 Newman-Conway Sequence
 
 [Newman-Conway sequence] is the one which generates the following integer sequence.  1 1 2 2 3 4 4 4 5 6 7 7….. and follows below recursive formula.

lib/max_subarray.rb

@@ -2,7 +2,49 @@
 # Time Complexity: ?
 # Space Complexity: ?
 def max_sub_array(nums)
-    return 0 if nums == nil
+    return nil if nums.nil? || nums.empty?
+    return nums[0] if nums.length == 1
+
+    current_max = global_max = nums[0]
+    index = 1
 
-    raise NotImplementedError, "Method not implemented yet!"
+    until index == nums.length
+        # binding.pry
+        if nums[index] > current_max + nums[index]
+            current_max = nums[index]
+        else
+            current_max += nums[index]
+        end
+
+        global_max = current_max if current_max > global_max
+        index += 1
+    end
+
+    return global_max
+
 end
+
+# Write a method to find the contiguous subarray in a 1-dimensional array with the largest sum.
+# This can be solved using Kadane's Algorithm
+
+# 
+
+# ```
+# Initialize:
+#     max_so_far = 0
+#     max_ending_here = 0
+
+# Loop for each element of the array
+#   (a) max_ending_here = max_ending_here + a[i]
+#   (b) if(max_ending_here < 0)
+#             max_ending_here = 0
+#   (c) if(max_so_far < max_ending_here)
+#             max_so_far = max_ending_here
+# return max_so_far
+# ```
+
+# ### Explanation
+
+# The idea of the Kadane’s algorithm is to look for all positive contiguous segments of the array (max_ending_here is used for this). And keep track of the maximum sum contiguous segment among all positive segments (max_so_far is used for this). Each time we get a positive sum compare it with max_so_far and update max_so_far if it is greater than max_so_far
+
+# There is also a subtle divide & conquer algorithm for this.

lib/newman_conway.rb

@@ -1,7 +1,34 @@
+require 'pry'
+# P(n) = P(P(n - 1)) + P(n - P(n - 1))
 
+# Eg 1
+# Input : 13
+# Output : 1 1 2 2 3 4 4 4 5 6 7 7 8
+
+# Input : 20
+# Output : 1 1 2 2 3 4 4 4 5 6 7 7 8 8 8 8 9 10 11 12
 
 # Time complexity: ?
 # Space Complexity: ?
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
-end
+
+  if num <= 0
+    raise ArgumentError.new
+  end
+
+  sequence = []
+
+  num.times do |i|
+
+    if i < 2
+      sequence << 1
+    else
+      prev = sequence[i - 1]
+      sequence << sequence[prev - 1] + sequence[i - prev]
+    end  
+  end
+
+  return sequence.join(" ")
+end
+
+

test/max_sub_array_test.rb

@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "max subarray" do
+describe "max subarray" do
   it "will work for [-2,1,-3,4,-1,2,1,-5,4]" do
     # Arrange
     input = [-2,1,-3,4,-1,2,1,-5,4]

test/newman_conway_test.rb

@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-describe "Newman Conway Tests" do
+xdescribe "Newman Conway Tests" do
   it "works with 13" do
     # Arrange
     input = 13