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66 lines
1.6 KiB
66 lines
1.6 KiB
=begin
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File: coin_change.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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### 零錢兌換：動態規劃 ###
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def coin_change_dp(coins, amt)
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n = coins.length
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_MAX = amt + 1
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# 初始化 dp 表
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dp = Array.new(n + 1) { Array.new(amt + 1, 0) }
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# 狀態轉移：首行首列
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(1...(amt + 1)).each { |a| dp[0][a] = _MAX }
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# 狀態轉移：其餘行和列
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for i in 1...(n + 1)
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for a in 1...(amt + 1)
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if coins[i - 1] > a
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# 若超過目標金額，則不選硬幣 i
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dp[i][a] = dp[i - 1][a]
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else
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# 不選和選硬幣 i 這兩種方案的較小值
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dp[i][a] = [dp[i - 1][a], dp[i][a - coins[i - 1]] + 1].min
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end
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end
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end
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dp[n][amt] != _MAX ? dp[n][amt] : -1
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end
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### 零錢兌換：空間最佳化後的動態規劃 ###
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def coin_change_dp_comp(coins, amt)
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n = coins.length
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_MAX = amt + 1
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# 初始化 dp 表
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dp = Array.new(amt + 1, _MAX)
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dp[0] = 0
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# 狀態轉移
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for i in 1...(n + 1)
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# 正序走訪
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for a in 1...(amt + 1)
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if coins[i - 1] > a
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# 若超過目標金額，則不選硬幣 i
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dp[a] = dp[a]
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else
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# 不選和選硬幣 i 這兩種方案的較小值
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dp[a] = [dp[a], dp[a - coins[i - 1]] + 1].min
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end
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end
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end
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dp[amt] != _MAX ? dp[amt] : -1
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end
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### Driver Code ###
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if __FILE__ == $0
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coins = [1, 2, 5]
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amt = 4
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# 動態規劃
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res = coin_change_dp(coins, amt)
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puts "湊到目標金額所需的最少硬幣數量為 #{res}"
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# 空間最佳化後的動態規劃
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res = coin_change_dp_comp(coins, amt)
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puts "湊到目標金額所需的最少硬幣數量為 #{res}"
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end
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