Additional Work on 384.rb

384.rb

@@ -1,46 +1,92 @@
-fibonacci = []
-seen = {}
-fibonacci[0] = 1
-fibonacci[1] = 1
+# substitution = {
+#   "1 1" => "1 1 1 -1",
+#   "1 -1" => "1 1 -1 1",
+#   "-1 1" => "-1 -1 1 -1",
+#   "-1 -1" => "-1 -1 -1 1"
+# }
+
+# string = "1 1 1 -1"
+
+# 1.upto(24) do
+#   parsed = string.scan(/-?\d\s-?\d/)
+#   string = string + " " + parsed.slice(parsed.size/2..parsed.size).map{|i| substitution[i]}.join(" ")
+# end
+
+# fibonacci_index = 2
+# t = 2
+# c = 1
+
+# sum = 0
+
+# string.split(/\s/).each_with_index do |number, index|
+#   sum += number.to_i
+#   if seen.include?(sum)
+#     seen[sum] += 1
+#     if sum == t and seen[sum] == c
+#       t_even = t % 2 == 0
+#       c_even = c % 2 == 0
+#       index_even = index % 2 == 0
+#       puts "g(#{t_even ? "E" : "O"}, #{c_even ? "E" : "O"}) = #{index_even ? "E" : "O"}"
+#       #puts "g(#{t}, #{c}) = #{index}"
+#       fibonacci_index += 1
+#       c = t
+#       t = fibonacci[fibonacci_index]
+#     end
+#   end
+# end
+require 'pp'
+
+@fibonacci = []
+@fibonacci[0] = 1
+@fibonacci[1] = 1
 
 2.upto(45) do |i|
-  fibonacci[i] = fibonacci[i-1] + fibonacci[i-2]
-  seen[fibonacci[i]] = 0
+  @fibonacci[i] = @fibonacci[i-1] + @fibonacci[i-2]
 end
 
-substitution = {
-  "1 1" => "1 1 1 -1",
-  "1 -1" => "1 1 -1 1",
-  "-1 1" => "-1 -1 1 -1",
-  "-1 -1" => "-1 -1 -1 1"
-}
+@sequence_a_lookup = {}
+@sequence_b_lookup = {}
+@summatory_sequence_index_lookup = {}
+@summatory_sequence_lookup = []
+@last_summatory_sequence = 0
+@last_summatory_index = 0
 
-string = "1 1 1 -1"
+def sequence_a(n)
+  @sequence_a_lookup[n] ||= b = n.to_s(2); b.count('1') - b.split(/0+/).count
+end
 
-1.upto(24) do
-  parsed = string.scan(/-?\d\s-?\d/)
-  string = string + " " + parsed.slice(parsed.size/2..parsed.size).map{|i| substitution[i]}.join(" ")
+def sequence_b(n)
+  @sequence_b_lookup[n] ||= (-1)**sequence_a(n)
 end
 
-fibonacci_index = 2
-t = 2
-c = 1
-
-sum = 0
-
-string.split(/\s/).each_with_index do |number, index|
-  sum += number.to_i
-  if seen.include?(sum)
-    seen[sum] += 1
-    if sum == t and seen[sum] == c
-      t_even = t % 2 == 0
-      c_even = c % 2 == 0
-      index_even = index % 2 == 0
-      puts "g(#{t_even ? "E" : "O"}, #{c_even ? "E" : "O"}) = #{index_even ? "E" : "O"}"
-      #puts "g(#{t}, #{c}) = #{index}"
-      fibonacci_index += 1
-      c = t
-      t = fibonacci[fibonacci_index]
+def summatory_sequence(n)
+  @summatory_sequence_lookup[n] || -> {
+    @last_summatory_index.upto(n) do |i|
+      @sum = @last_summatory_sequence + sequence_b(i)
+
+      @last_summatory_sequence = @sum
+      @summatory_sequence_lookup << @sum
+      if @summatory_sequence_index_lookup[@sum]
+        @summatory_sequence_index_lookup[@sum] << @last_summatory_index
+      else
+        @summatory_sequence_index_lookup[@sum] = [@last_summatory_index]
+      end
+      @last_summatory_index += 1
     end
+    @sum
+  }.call
+end
+
+def g_t_c(t, c)
+  if @summatory_sequence_index_lookup[t].nil? || @summatory_sequence_index_lookup[t][c-1].nil?
+    summatory_sequence(t*t)
   end
-end
+  @summatory_sequence_index_lookup[t][c-1]
+end
+
+pp g_t_c(100,1)
+# seq = []
+# 1.upto(15) do |i|
+#   seq << g_t_c(i, 1)
+# end
+# pp seq.join(", ")