Using Hash as Recursive Function with Memoization

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We can define a new Hash in a smart way by using Hash#new and passing it a block:

h    = Hash.new {|hash,key| hash[key] = hash[key-1] + hash[key-2]}
h[1] = 0
h[2] = 1

puts h[3] #=> 1
puts h[100] #=> 218922995834555169026

Here an example of famous Collatz Conjecture:

h    = Hash.new {|hash,n| hash[n] = 1 + (n.odd? ? hash[3*n+1] : hash[n/2])}
h[1] = 1

puts h[100] #=> 26
puts h[1000] #=> 112

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