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41 lines
899 B
41 lines
899 B
=begin
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File: climbing_stairs_dp.rb
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Created Time: 2024-05-29
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Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
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=end
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### 爬樓梯：動態規劃 ###
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def climbing_stairs_dp(n)
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return n if n == 1 || n == 2
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# 初始化 dp 表，用於儲存子問題的解
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dp = Array.new(n + 1, 0)
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# 初始狀態：預設最小子問題的解
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dp[1], dp[2] = 1, 2
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# 狀態轉移：從較小子問題逐步求解較大子問題
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(3...(n + 1)).each { |i| dp[i] = dp[i - 1] + dp[i - 2] }
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dp[n]
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end
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### 爬樓梯：空間最佳化後的動態規劃 ###
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def climbing_stairs_dp_comp(n)
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return n if n == 1 || n == 2
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a, b = 1, 2
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(3...(n + 1)).each { a, b = b, a + b }
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b
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end
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### Driver Code ###
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if __FILE__ == $0
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n = 9
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res = climbing_stairs_dp(n)
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puts "爬 #{n} 階樓梯共有 #{res} 種方案"
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res = climbing_stairs_dp_comp(n)
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puts "爬 #{n} 階樓梯共有 #{res} 種方案"
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end
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