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krahets
2024-05-31 12:45:17 +08:00
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docs/chapter_dynamic_programming/unbounded_knapsack_problem.md
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@@ -350,7 +350,25 @@ $$
=== "Ruby"
```ruby title="unbounded_knapsack.rb"
[class]{}-[func]{unbounded_knapsack_dp}
### 完全背包：动态规划 ###
def unbounded_knapsack_dp(wgt, val, cap)
n = wgt.length
# 初始化 dp 表
dp = Array.new(n + 1) { Array.new(cap + 1, 0) }
# 状态转移
for i in 1...(n + 1)
for c in 1...(cap + 1)
if wgt[i - 1] > c
# 若超过背包容量，则不选物品 i
dp[i][c] = dp[i - 1][c]
else
# 不选和选物品 i 这两种方案的较大值
dp[i][c] = [dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]].max
end
end
end
dp[n][cap]
end
```
=== "Zig"
@@ -709,7 +727,46 @@ $$
=== "Ruby"
```ruby title="unbounded_knapsack.rb"
[class]{}-[func]{unbounded_knapsack_dp_comp}
### 完全背包：动态规划 ###
def unbounded_knapsack_dp(wgt, val, cap)
n = wgt.length
# 初始化 dp 表
dp = Array.new(n + 1) { Array.new(cap + 1, 0) }
# 状态转移
for i in 1...(n + 1)
for c in 1...(cap + 1)
if wgt[i - 1] > c
# 若超过背包容量，则不选物品 i
dp[i][c] = dp[i - 1][c]
else
# 不选和选物品 i 这两种方案的较大值
dp[i][c] = [dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]].max
end
end
end
dp[n][cap]
end
### 完全背包：空间优化后的动态规划 ##3
def unbounded_knapsack_dp_comp(wgt, val, cap)
n = wgt.length
# 初始化 dp 表
dp = Array.new(cap + 1, 0)
# 状态转移
for i in 1...(n + 1)
# 正序遍历
for c in 1...(cap + 1)
if wgt[i -1] > c
# 若超过背包容量，则不选物品 i
dp[c] = dp[c]
else
# 不选和选物品 i 这两种方案的较大值
dp[c] = [dp[c], dp[c - wgt[i - 1]] + val[i - 1]].max
end
end
end
dp[cap]
end
```
=== "Zig"
@@ -1159,7 +1216,28 @@ $$
=== "Ruby"
```ruby title="coin_change.rb"
[class]{}-[func]{coin_change_dp}
### 零钱兑换：动态规划 ###
def coin_change_dp(coins, amt)
n = coins.length
_MAX = amt + 1
# 初始化 dp 表
dp = Array.new(n + 1) { Array.new(amt + 1, 0) }
# 状态转移：首行首列
(1...(amt + 1)).each { |a| dp[0][a] = _MAX }
# 状态转移：其余行和列
for i in 1...(n + 1)
for a in 1...(amt + 1)
if coins[i - 1] > a
# 若超过目标金额，则不选硬币 i
dp[i][a] = dp[i - 1][a]
else
# 不选和选硬币 i 这两种方案的较小值
dp[i][a] = [dp[i - 1][a], dp[i][a - coins[i - 1]] + 1].min
end
end
end
dp[n][amt] != _MAX ? dp[n][amt] : -1
end
```
=== "Zig"
@@ -1586,7 +1664,28 @@ $$
=== "Ruby"
```ruby title="coin_change.rb"
[class]{}-[func]{coin_change_dp_comp}
### 零钱兑换：空间优化后的动态规划 ###
def coin_change_dp_comp(coins, amt)
n = coins.length
_MAX = amt + 1
# 初始化 dp 表
dp = Array.new(amt + 1, _MAX)
dp[0] = 0
# 状态转移
for i in 1...(n + 1)
# 正序遍历
for a in 1...(amt + 1)
if coins[i - 1] > a
# 若超过目标金额，则不选硬币 i
dp[a] = dp[a]
else
# 不选和选硬币 i 这两种方案的较小值
dp[a] = [dp[a], dp[a - coins[i - 1]] + 1].min
end
end
end
dp[amt] != _MAX ? dp[amt] : -1
end
```
=== "Zig"
@@ -1999,7 +2098,27 @@ $$
=== "Ruby"
```ruby title="coin_change_ii.rb"
[class]{}-[func]{coin_change_ii_dp}
### 零钱兑换 II：动态规划 ###
def coin_change_ii_dp(coins, amt)
n = coins.length
# 初始化 dp 表
dp = Array.new(n + 1) { Array.new(amt + 1, 0) }
# 初始化首列
(0...(n + 1)).each { |i| dp[i][0] = 1 }
# 状态转移
for i in 1...(n + 1)
for a in 1...(amt + 1)
if coins[i - 1] > a
# 若超过目标金额，则不选硬币 i
dp[i][a] = dp[i - 1][a]
else
# 不选和选硬币 i 这两种方案之和
dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]
end
end
end
dp[n][amt]
end
```
=== "Zig"
@@ -2343,7 +2462,27 @@ $$
=== "Ruby"
```ruby title="coin_change_ii.rb"
[class]{}-[func]{coin_change_ii_dp_comp}
### 零钱兑换 II：空间优化后的动态规划 ###
def coin_change_ii_dp_comp(coins, amt)
n = coins.length
# 初始化 dp 表
dp = Array.new(amt + 1, 0)
dp[0] = 1
# 状态转移
for i in 1...(n + 1)
# 正序遍历
for a in 1...(amt + 1)
if coins[i - 1] > a
# 若超过目标金额，则不选硬币 i
dp[a] = dp[a]
else
# 不选和选硬币 i 这两种方案之和
dp[a] = dp[a] + dp[a - coins[i - 1]]
end
end
end
dp[amt]
end
```
=== "Zig"