mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 20:46:28 +08:00
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.
99 lines
2.9 KiB
Ruby
99 lines
2.9 KiB
Ruby
=begin
|
|
File: knapsack.rb
|
|
Created Time: 2024-05-29
|
|
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
|
=end
|
|
|
|
### 0-1 背包：暴力搜尋 ###
|
|
def knapsack_dfs(wgt, val, i, c)
|
|
# 若已選完所有物品或背包無剩餘容量，則返回價值 0
|
|
return 0 if i == 0 || c == 0
|
|
# 若超過背包容量，則只能選擇不放入背包
|
|
return knapsack_dfs(wgt, val, i - 1, c) if wgt[i - 1] > c
|
|
# 計算不放入和放入物品 i 的最大價值
|
|
no = knapsack_dfs(wgt, val, i - 1, c)
|
|
yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]
|
|
# 返回兩種方案中價值更大的那一個
|
|
[no, yes].max
|
|
end
|
|
|
|
### 0-1 背包：記憶化搜尋 ###
|
|
def knapsack_dfs_mem(wgt, val, mem, i, c)
|
|
# 若已選完所有物品或背包無剩餘容量，則返回價值 0
|
|
return 0 if i == 0 || c == 0
|
|
# 若已有記錄，則直接返回
|
|
return mem[i][c] if mem[i][c] != -1
|
|
# 若超過背包容量，則只能選擇不放入背包
|
|
return knapsack_dfs_mem(wgt, val, mem, i - 1, c) if wgt[i - 1] > c
|
|
# 計算不放入和放入物品 i 的最大價值
|
|
no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)
|
|
yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]
|
|
# 記錄並返回兩種方案中價值更大的那一個
|
|
mem[i][c] = [no, yes].max
|
|
end
|
|
|
|
### 0-1 背包：動態規劃 ###
|
|
def knapsack_dp(wgt, val, cap)
|
|
n = wgt.length
|
|
# 初始化 dp 表
|
|
dp = Array.new(n + 1) { Array.new(cap + 1, 0) }
|
|
# 狀態轉移
|
|
for i in 1...(n + 1)
|
|
for c in 1...(cap + 1)
|
|
if wgt[i - 1] > c
|
|
# 若超過背包容量，則不選物品 i
|
|
dp[i][c] = dp[i - 1][c]
|
|
else
|
|
# 不選和選物品 i 這兩種方案的較大值
|
|
dp[i][c] = [dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]].max
|
|
end
|
|
end
|
|
end
|
|
dp[n][cap]
|
|
end
|
|
|
|
### 0-1 背包：空間最佳化後的動態規劃 ###
|
|
def knapsack_dp_comp(wgt, val, cap)
|
|
n = wgt.length
|
|
# 初始化 dp 表
|
|
dp = Array.new(cap + 1, 0)
|
|
# 狀態轉移
|
|
for i in 1...(n + 1)
|
|
# 倒序走訪
|
|
for c in cap.downto(1)
|
|
if wgt[i - 1] > c
|
|
# 若超過背包容量，則不選物品 i
|
|
dp[c] = dp[c]
|
|
else
|
|
# 不選和選物品 i 這兩種方案的較大值
|
|
dp[c] = [dp[c], dp[c - wgt[i - 1]] + val[i - 1]].max
|
|
end
|
|
end
|
|
end
|
|
dp[cap]
|
|
end
|
|
|
|
### Driver Code ###
|
|
if __FILE__ == $0
|
|
wgt = [10, 20, 30, 40, 50]
|
|
val = [50, 120, 150, 210, 240]
|
|
cap = 50
|
|
n = wgt.length
|
|
|
|
# 暴力搜尋
|
|
res = knapsack_dfs(wgt, val, n, cap)
|
|
puts "不超過背包容量的最大物品價值為 #{res}"
|
|
|
|
# 記憶化搜尋
|
|
mem = Array.new(n + 1) { Array.new(cap + 1, -1) }
|
|
res = knapsack_dfs_mem(wgt, val, mem, n, cap)
|
|
puts "不超過背包容量的最大物品價值為 #{res}"
|
|
|
|
# 動態規劃
|
|
res = knapsack_dp(wgt, val, cap)
|
|
puts "不超過背包容量的最大物品價值為 #{res}"
|
|
|
|
# 空間最佳化後的動態規劃
|
|
res = knapsack_dp_comp(wgt, val, cap)
|
|
puts "不超過背包容量的最大物品價值為 #{res}"
|
|
end
|