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* Retranslate the complete English edition from Simplified Chinese * Polish three English explanations after reader-focused review
100 lines
3.2 KiB
Ruby
100 lines
3.2 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 knapsack: brute-force search ###
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def knapsack_dfs(wgt, val, i, c)
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# If all items have been considered or no capacity remains, return value 0
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return 0 if i == 0 || c == 0
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# If the item exceeds the remaining capacity, it must be excluded
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return knapsack_dfs(wgt, val, i - 1, c) if wgt[i - 1] > c
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# Calculate the maximum values obtained by excluding and including item i
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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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# Return the larger value from the two choices
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[no, yes].max
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end
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### 0-1 knapsack: memoized search ###
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def knapsack_dfs_mem(wgt, val, mem, i, c)
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# If all items have been considered or no capacity remains, return value 0
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return 0 if i == 0 || c == 0
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# If a result has already been recorded, return it directly
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return mem[i][c] if mem[i][c] != -1
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# If the item exceeds the remaining capacity, it must be excluded
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return knapsack_dfs_mem(wgt, val, mem, i - 1, c) if wgt[i - 1] > c
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# Calculate the maximum values obtained by excluding and including item i
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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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# Record and return the larger value from the two choices
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mem[i][c] = [no, yes].max
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end
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### 0-1 knapsack: dynamic programming ###
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def knapsack_dp(wgt, val, cap)
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n = wgt.length
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# Initialize the dp table
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dp = Array.new(n + 1) { Array.new(cap + 1, 0) }
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# State transitions
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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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# If item i exceeds the remaining capacity, do not choose it
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dp[i][c] = dp[i - 1][c]
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else
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# Take the larger value obtained by excluding and including item i
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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 knapsack: space-optimized dynamic programming ###
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def knapsack_dp_comp(wgt, val, cap)
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n = wgt.length
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# Initialize the dp table
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dp = Array.new(cap + 1, 0)
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# State transitions
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for i in 1...(n + 1)
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# Traverse in decreasing order
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for c in cap.downto(1)
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if wgt[i - 1] > c
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# If item i exceeds the remaining capacity, do not choose it
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dp[c] = dp[c]
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else
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# Take the larger value obtained by excluding and including item i
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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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# Brute-force search
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res = knapsack_dfs(wgt, val, n, cap)
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puts "Maximum total item value within the knapsack capacity: #{res}"
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# Memoized search
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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 "Maximum total item value within the knapsack capacity: #{res}"
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# Dynamic programming
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res = knapsack_dp(wgt, val, cap)
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puts "Maximum total item value within the knapsack capacity: #{res}"
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# Space-optimized dynamic programming
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res = knapsack_dp_comp(wgt, val, cap)
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puts "Maximum total item value within the knapsack capacity: #{res}"
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end
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