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3f4220de81
* preorder, inorder, postorder -> pre-order, in-order, post-order * Bug fixes * Bug fixes * Update what_is_dsa.md * Sync zh and zh-hant versions * Sync zh and zh-hant versions. * Update performance_evaluation.md and time_complexity.md * Add @khoaxuantu to the landing page. * Sync zh and zh-hant versions * Add @ khoaxuantu to the landing page of zh-hant and en versions.
100 lines
2.9 KiB
Ruby
100 lines
2.9 KiB
Ruby
=begin
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File: 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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### 0-1 背包：暴力搜尋 ###
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def knapsack_dfs(wgt, val, i, c)
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# 若已選完所有物品或背包無剩餘容量，則返回價值 0
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return 0 if i == 0 || c == 0
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# 若超過背包容量，則只能選擇不放入背包
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return knapsack_dfs(wgt, val, i - 1, c) if wgt[i - 1] > c
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# 計算不放入和放入物品 i 的最大價值
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no = knapsack_dfs(wgt, val, i - 1, c)
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yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]
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# 返回兩種方案中價值更大的那一個
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[no, yes].max
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end
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### 0-1 背包：記憶化搜尋 ###
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def knapsack_dfs_mem(wgt, val, mem, i, c)
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# 若已選完所有物品或背包無剩餘容量，則返回價值 0
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return 0 if i == 0 || c == 0
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# 若已有記錄，則直接返回
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return mem[i][c] if mem[i][c] != -1
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# 若超過背包容量，則只能選擇不放入背包
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return knapsack_dfs_mem(wgt, val, mem, i - 1, c) if wgt[i - 1] > c
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# 計算不放入和放入物品 i 的最大價值
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no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)
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yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]
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# 記錄並返回兩種方案中價值更大的那一個
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mem[i][c] = [no, yes].max
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end
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### 0-1 背包：動態規劃 ###
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def 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 - 1][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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### 0-1 背包：空間最佳化後的動態規劃 ###
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def 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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# 倒序走訪
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for c in cap.downto(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 = [10, 20, 30, 40, 50]
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val = [50, 120, 150, 210, 240]
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cap = 50
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n = wgt.length
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# 暴力搜尋
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res = knapsack_dfs(wgt, val, n, 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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# 記憶化搜尋
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mem = Array.new(n + 1) { Array.new(cap + 1, -1) }
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res = knapsack_dfs_mem(wgt, val, mem, n, 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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# 動態規劃
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res = 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 = 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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