[feat] add ruby code - chapter dynamic programming

codes/ruby/chapter_dynamic_programming/climbing_stairs_backtrack.rb

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+=begin
+File: climbing_stairs_backtrack.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen ([email protected])
+=end
+
+### 回溯 ###
+def backtrack(choices, state, n, res)
+  # 当爬到第 n 阶时，方案数量加 1
+  res[0] += 1 if state == n
+  # 遍历所有选择
+  for choice in choices
+    # 剪枝：不允许越过第 n 阶
+    next if state + choice > n
+
+    # 尝试：做出选择，更新状态
+    backtrack(choices, state + choice, n, res)
+  end
+  # 回退
+end
+
+### 爬楼梯：回溯 ###
+def climbing_stairs_backtrack(n)
+  choices = [1, 2] # 可选择向上爬 1 阶或 2 阶
+  state = 0 # 从第 0 阶开始爬
+  res = [0] # 使用 res[0] 记录方案数量
+  backtrack(choices, state, n, res)
+  res.first
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  n = 9
+
+  res = climbing_stairs_backtrack(n)
+  puts "爬 #{n} 阶楼梯共有 #{res} 种方案"
+end

codes/ruby/chapter_dynamic_programming/climbing_stairs_constraint_dp.rb

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+=begin
+File: climbing_stairs_constraint_dp.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen ([email protected])
+=end
+
+### 带约束爬楼梯：动态规划 ###
+def climbing_stairs_backtrack(n)
+  return 1 if n == 1 || n == 2
+
+  # 初始化 dp 表，用于存储子问题的解
+  dp = Array.new(n + 1) { Array.new(3, 0) }
+  # 初始状态：预设最小子问题的解
+  dp[1][1], dp[1][2] = 1, 0
+  dp[2][1], dp[2][2] = 0, 1
+  # 状态转移：从较小子问题逐步求解较大子问题
+  for i in 3...(n + 1)
+    dp[i][1] = dp[i - 1][2]
+    dp[i][2] = dp[i - 2][1] + dp[i - 2][2]
+  end
+
+  dp[n][1] + dp[n][2]
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  n = 9
+
+  res = climbing_stairs_backtrack(n)
+  puts "爬 #{n} 阶楼梯共有 #{res} 种方案"
+end

codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs.rb

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+=begin
+File: climbing_stairs_dfs.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen ([email protected])
+=end
+
+### 搜索 ###
+def dfs(i)
+  # 已知 dp[1] 和 dp[2] ，返回之
+  return i if i == 1 || i == 2
+  # dp[i] = dp[i-1] + dp[i-2]
+  dfs(i - 1) + dfs(i - 2)
+end
+
+### 爬楼梯：搜索 ###
+def climbing_stairs_dfs(n)
+  dfs(n)
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  n = 9
+
+  res = climbing_stairs_dfs(n)
+  puts "爬 #{n} 阶楼梯共有 #{res} 种方案"
+end

codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs_mem.rb

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+=begin
+File: climbing_stairs_dfs_mem.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen ([email protected])
+=end
+
+### 记忆化搜索 ###
+def dfs(i, mem)
+  # 已知 dp[1] 和 dp[2] ，返回之
+  return i if i == 1 || i == 2
+  # 若存在记录 dp[i] ，则直接返回之
+  return mem[i] if mem[i] != -1
+
+  # dp[i] = dp[i-1] + dp[i-2]
+  count = dfs(i - 1, mem) + dfs(i - 2, mem)
+  # 记录 dp[i]
+  mem[i] = count
+end
+
+### 爬楼梯：记忆化搜索 ###
+def climbing_stairs_dfs_mem(n)
+  # mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
+  mem = Array.new(n + 1, -1)
+  dfs(n, mem)
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  n = 9
+
+  res = climbing_stairs_dfs_mem(n)
+  puts "爬 #{n} 阶楼梯共有 #{res} 种方案"
+end

codes/ruby/chapter_dynamic_programming/climbing_stairs_dp.rb

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+=begin
+File: climbing_stairs_dp.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen ([email protected])
+=end
+
+### 爬楼梯：动态规划 ###
+def climbing_stairs_dp(n)
+  return n  if n == 1 || n == 2
+
+  # 初始化 dp 表，用于存储子问题的解
+  dp = Array.new(n + 1, 0)
+  # 初始状态：预设最小子问题的解
+  dp[1], dp[2] = 1, 2
+  # 状态转移：从较小子问题逐步求解较大子问题
+  (3...(n + 1)).each { |i| dp[i] = dp[i - 1] + dp[i - 2] }
+
+  dp[n]
+end
+
+### 爬楼梯：空间优化后的动态规划 ###
+def climbing_stairs_dp_comp(n)
+  return n if n == 1 || n == 2
+
+  a, b = 1, 2
+  (3...(n + 1)).each { a, b = b, a + b }
+
+  b
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  n = 9
+
+  res = climbing_stairs_dp(n)
+  puts "爬 #{n} 阶楼梯共有 #{res} 种方案"
+
+  res = climbing_stairs_dp_comp(n)
+  puts "爬 #{n} 阶楼梯共有 #{res} 种方案"
+end

codes/ruby/chapter_dynamic_programming/coin_change.rb

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+=begin
+File: coin_change.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen ([email protected])
+=end
+
+### 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
+
+### 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
+
+### Driver Code ###
+if __FILE__ == $0
+  coins = [1, 2, 5]
+  amt = 4
+
+  # 动态规划
+  res = coin_change_dp(coins, amt)
+  puts "凑到目标金额所需的最少硬币数量为 #{res}"
+
+  # 空间优化后的动态规划
+  res = coin_change_dp_comp(coins, amt)
+  puts "凑到目标金额所需的最少硬币数量为 #{res}"
+end

codes/ruby/chapter_dynamic_programming/coin_change_ii.rb

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+=begin
+File: coin_change_ii.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen ([email protected])
+=end
+
+### 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
+
+### 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
+
+### Driver Code ###
+if __FILE__ == $0
+  coins = [1, 2, 5]
+  amt = 5
+
+  # 动态规划
+  res = coin_change_ii_dp(coins, amt)
+  puts "凑出目标金额的硬币组合数量为 #{res}"
+
+  # 空间优化后的动态规划
+  res = coin_change_ii_dp_comp(coins, amt)
+  puts "凑出目标金额的硬币组合数量为 #{res}"
+end