Time - Yolotzin

lib/max_subarray.rb

@@ -1,8 +1,43 @@
 
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(n)
+# Space Complexity: O(1)
 def max_sub_array(nums)
-    return 0 if nums == nil
-
-    raise NotImplementedError, "Method not implemented yet!"
+    return nil if nums == nil || nums.empty?
+    return nums[0] if nums.length == 1
+    max = nums[0] # start with first element and then skip in loop
+    current = nums[0]
+    i = 1
+    while i < nums.length 
+        current += nums[i]
+        if max < current
+            max = current
+        end
+        if current < 0
+            current = 0
+        end
+        i += 1
+    end
+    return 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
+
+# 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 +1,39 @@
 
 
-# Time complexity: ?
-# Space Complexity: ?
+# Time complexity: O(n)
+# Space Complexity: O(n)
 def newman_conway(num)
-  raise NotImplementedError, "newman_conway isn't implemented"
-end
+  raise ArgumentError, 'must be number > 0' if num == 0 
+  return "1" if num == 1
+  array = Array.new(num)
+  array[0] = 0
+  array[1] = 1
+  array[2] = 1
+  i = 3
+  while i <= num
+    array[i] = array[array[i - 1]] + array[i - array[i - 1]]
+    i += 1
+  end
+  return array[1..num].join(' ')
+end
+
+
+# [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.
+
+# P(1) = 1
+# P(2) = 1
+# for all n > 2
+# P(n) = P(P(n - 1)) + P(n - P(n - 1))
+# Given a number n then print n terms of Newman-Conway Sequence
+
+# Examples:
+
+# 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
+# You should be able to do this in O(n) time complexity.
+

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]