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62 lines
1.5 KiB
62 lines
1.5 KiB
=begin
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File: unbounded_knapsack.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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### 完全背包：動態規劃 ###
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def unbounded_knapsack_dp(wgt, val, cap)
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n = wgt.length
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# 初始化 dp 表
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dp = Array.new(n + 1) { Array.new(cap + 1, 0) }
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# 狀態轉移
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for i in 1...(n + 1)
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for c in 1...(cap + 1)
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if wgt[i - 1] > c
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# 若超過背包容量，則不選物品 i
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dp[i][c] = dp[i - 1][c]
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else
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# 不選和選物品 i 這兩種方案的較大值
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dp[i][c] = [dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]].max
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end
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end
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end
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dp[n][cap]
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end
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### 完全背包：空間最佳化後的動態規劃 ##3
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def unbounded_knapsack_dp_comp(wgt, val, cap)
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n = wgt.length
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# 初始化 dp 表
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dp = Array.new(cap + 1, 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 c in 1...(cap + 1)
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if wgt[i -1] > c
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# 若超過背包容量，則不選物品 i
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dp[c] = dp[c]
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else
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# 不選和選物品 i 這兩種方案的較大值
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dp[c] = [dp[c], dp[c - wgt[i - 1]] + val[i - 1]].max
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end
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end
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end
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dp[cap]
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end
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### Driver Code ###
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if __FILE__ == $0
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wgt = [1, 2, 3]
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val = [5, 11, 15]
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cap = 4
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# 動態規劃
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res = unbounded_knapsack_dp(wgt, val, cap)
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puts "不超過背包容量的最大物品價值為 #{res}"
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# 空間最佳化後的動態規劃
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res = unbounded_knapsack_dp_comp(wgt, val, cap)
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puts "不超過背包容量的最大物品價值為 #{res}"
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end
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