mirror of
https://github.com/TheAlgorithms/Ruby
synced 2024-12-26 21:58:56 +01:00
53 lines
1.2 KiB
Ruby
53 lines
1.2 KiB
Ruby
# The Fibonacci numbers, commonly denoted F(n) form a sequence,
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# called the Fibonacci sequence, such that # each number is the sum
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# of the two preceding ones, starting from 0 and 1. That is,
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#
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# F(0) = 0, F(1) = 1
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# F(n) = F(n - 1) + F(n - 2), for n > 1
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#
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# Given n, calculate F(n).
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#
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# Approach: Top-Down Approach using Memoization
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#
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# Complexity Analysis:
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#
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# Time complexity: O(n). Each number, starting at 2 up to and
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# including N, is visited, computed and then stored for O(1) access
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# later on.
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#
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# Space complexity: O(n). The size of the stack in memory is
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# proportionate to N.
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#
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def fibonacci(number, memo_hash = {})
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return number if number <= 1
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memo_hash[0] = 0
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memo_hash[1] = 1
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memoize(number, memo_hash)
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end
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def memoize(number, memo_hash)
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return memo_hash[number] if memo_hash.keys.include? number
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memo_hash[number] = memoize(number - 1, memo_hash) + memoize(number - 2, memo_hash)
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memoize(number, memo_hash)
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end
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n = 2
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fibonacci(n)
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# Output: 1
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# Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.
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n = 3
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fibonacci(n)
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# Output: 2
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# Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.
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n = 4
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fibonacci(n)
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# Output: 3
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# Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.
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