task3 solution (without priority queue)

Author: proton

week4/priority-queues/task3/solution.rb

@@ -1,12 +1,3 @@
-### Taxicab numbers
-
-# A `taxicab` number is an integer that can be expressed as the sum of two cubes of positive integers in two different ways: `a^3 + b^3 = c^3 + d^3`.
-# For example, `1729` is the smallest taxicab number: `9^3 + 10^3 = 1^3 + 12^3`.
-# Design an algorithm to find all taxicab numbers with `a`, `b`, `c`, and `d` less than `n`.
-
-# - Version 1: Use time proportional to `(n^2)*log(n)` and space proportional to `n^2`.
-# - Version 2: Use time proportional to `(n^2)*log(n)` and space proportional to `n`.
-
 def baseline(n)
   arr = []
 
@@ -26,4 +17,24 @@ def baseline(n)
   arr.sort.uniq
 end
 
+def solution(n)
+  # n
+  numbers = (1...n).map { |i| i**3 }
+
+  # n^2
+  h = {}
+  numbers.each_with_index do |a, i|
+  ((i + 1)...(n - 1)).each do |j|
+    b = numbers[j]
+    s = a + b
+    h[s] ||= []
+    h[s] << [a, b]
+  end
+  end
+
+  h = h.select { |k, v| v.size > 1 }
+  h.keys
+end
+
 p baseline(30)
+p solution(30)