From a14be17b74dd19ed33297071feeecbc07d2a8cd7 Mon Sep 17 00:00:00 2001
From: khoaxuantu <68913255+khoaxuantu@users.noreply.github.com>
Date: Thu, 30 May 2024 16:11:56 +0700
Subject: [PATCH] [feat] add ruby code - chapter dynamic programming (#1378)

---
 .../climbing_stairs_backtrack.rb              |  37 ++++++
 .../climbing_stairs_constraint_dp.rb          |  31 +++++
 .../climbing_stairs_dfs.rb                    |  26 ++++
 .../climbing_stairs_dfs_mem.rb                |  33 +++++
 .../climbing_stairs_dp.rb                     |  40 ++++++
 .../coin_change.rb                            |  65 ++++++++++
 .../coin_change_ii.rb                         |  63 ++++++++++
 .../edit_distance.rb                          | 115 ++++++++++++++++++
 .../chapter_dynamic_programming/knapsack.rb   |  99 +++++++++++++++
 .../min_cost_climbing_stairs_dp.rb            |  39 ++++++
 .../min_path_sum.rb                           |  93 ++++++++++++++
 .../unbounded_knapsack.rb                     |  61 ++++++++++
 12 files changed, 702 insertions(+)
 create mode 100644 codes/ruby/chapter_dynamic_programming/climbing_stairs_backtrack.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/climbing_stairs_constraint_dp.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs_mem.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/climbing_stairs_dp.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/coin_change.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/coin_change_ii.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/edit_distance.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/knapsack.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/min_cost_climbing_stairs_dp.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/min_path_sum.rb
 create mode 100644 codes/ruby/chapter_dynamic_programming/unbounded_knapsack.rb

diff --git a/codes/ruby/chapter_dynamic_programming/climbing_stairs_backtrack.rb b/codes/ruby/chapter_dynamic_programming/climbing_stairs_backtrack.rb
new file mode 100644
index 000000000..ad0e02bef
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/climbing_stairs_backtrack.rb
@@ -0,0 +1,37 @@
+=begin
+File: climbing_stairs_backtrack.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=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
diff --git a/codes/ruby/chapter_dynamic_programming/climbing_stairs_constraint_dp.rb b/codes/ruby/chapter_dynamic_programming/climbing_stairs_constraint_dp.rb
new file mode 100644
index 000000000..1421d09f5
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/climbing_stairs_constraint_dp.rb
@@ -0,0 +1,31 @@
+=begin
+File: climbing_stairs_constraint_dp.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=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
diff --git a/codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs.rb b/codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs.rb
new file mode 100644
index 000000000..ed9b2b39f
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs.rb
@@ -0,0 +1,26 @@
+=begin
+File: climbing_stairs_dfs.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=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
diff --git a/codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs_mem.rb b/codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs_mem.rb
new file mode 100644
index 000000000..502e9563e
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/climbing_stairs_dfs_mem.rb
@@ -0,0 +1,33 @@
+=begin
+File: climbing_stairs_dfs_mem.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=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
diff --git a/codes/ruby/chapter_dynamic_programming/climbing_stairs_dp.rb b/codes/ruby/chapter_dynamic_programming/climbing_stairs_dp.rb
new file mode 100644
index 000000000..a88abb4d1
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/climbing_stairs_dp.rb
@@ -0,0 +1,40 @@
+=begin
+File: climbing_stairs_dp.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=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
diff --git a/codes/ruby/chapter_dynamic_programming/coin_change.rb b/codes/ruby/chapter_dynamic_programming/coin_change.rb
new file mode 100644
index 000000000..5135c0f5c
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/coin_change.rb
@@ -0,0 +1,65 @@
+=begin
+File: coin_change.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=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
diff --git a/codes/ruby/chapter_dynamic_programming/coin_change_ii.rb b/codes/ruby/chapter_dynamic_programming/coin_change_ii.rb
new file mode 100644
index 000000000..18cd0475b
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/coin_change_ii.rb
@@ -0,0 +1,63 @@
+=begin
+File: coin_change_ii.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=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
diff --git a/codes/ruby/chapter_dynamic_programming/edit_distance.rb b/codes/ruby/chapter_dynamic_programming/edit_distance.rb
new file mode 100644
index 000000000..67c6da916
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/edit_distance.rb
@@ -0,0 +1,115 @@
+=begin
+File: edit_distance.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### 编辑距离：暴力搜索 ###
+def edit_distance_dfs(s, t, i, j)
+  # 若 s 和 t 都为空，则返回 0
+  return 0 if i == 0 && j == 0
+  # 若 s 为空，则返回 t 长度
+  return j if i == 0
+  # 若 t 为空，则返回 s 长度
+  return i if j == 0
+  # 若两字符相等，则直接跳过此两字符
+  return edit_distance_dfs(s, t, i - 1, j - 1) if s[i - 1] == t[j - 1]
+  # 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
+  insert = edit_distance_dfs(s, t, i, j - 1)
+  delete = edit_distance_dfs(s, t, i - 1, j)
+  replace = edit_distance_dfs(s, t, i - 1, j - 1)
+  # 返回最少编辑步数
+  [insert, delete, replace].min + 1
+end
+
+def edit_distance_dfs_mem(s, t, mem, i, j)
+  # 若 s 和 t 都为空，则返回 0
+  return 0 if i == 0 && j == 0
+  # 若 s 为空，则返回 t 长度
+  return j if i == 0
+  # 若 t 为空，则返回 s 长度
+  return i if j == 0
+  # 若已有记录，则直接返回之
+  return mem[i][j] if mem[i][j] != -1
+  # 若两字符相等，则直接跳过此两字符
+  return edit_distance_dfs_mem(s, t, mem, i - 1, j - 1) if s[i - 1] == t[j - 1]
+  # 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
+  insert = edit_distance_dfs_mem(s, t, mem, i, j - 1)
+  delete = edit_distance_dfs_mem(s, t, mem, i - 1, j)
+  replace = edit_distance_dfs_mem(s, t, mem, i - 1, j - 1)
+  # 记录并返回最少编辑步数
+  mem[i][j] = [insert, delete, replace].min + 1
+end
+
+### 编辑距离：动态规划 ###
+def edit_distance_dp(s, t)
+  n, m = s.length, t.length
+  dp = Array.new(n + 1) { Array.new(m + 1, 0) }
+  # 状态转移：首行首列
+  (1...(n + 1)).each { |i| dp[i][0] = i }
+  (1...(m + 1)).each { |j| dp[0][j] = j }
+  # 状态转移：其余行和列
+  for i in 1...(n + 1)
+    for j in 1...(m +1)
+      if s[i - 1] == t[j - 1]
+        # 若两字符相等，则直接跳过此两字符
+        dp[i][j] = dp[i - 1][j - 1]
+      else
+        # 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
+        dp[i][j] = [dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]].min + 1
+      end
+    end
+  end
+  dp[n][m]
+end
+
+### 编辑距离：空间优化后的动态规划 ###
+def edit_distance_dp_comp(s, t)
+  n, m = s.length, t.length
+  dp = Array.new(m + 1, 0)
+  # 状态转移：首行
+  (1...(m + 1)).each { |j| dp[j] = j }
+  # 状态转移：其余行
+  for i in 1...(n + 1)
+    # 状态转移：首列
+    leftup = dp.first # 暂存 dp[i-1, j-1]
+    dp[0] += 1
+    # 状态转移：其余列
+    for j in 1...(m + 1)
+      temp = dp[j]
+      if s[i - 1] == t[j - 1]
+        # 若两字符相等，则直接跳过此两字符
+        dp[j] = leftup
+      else
+        # 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
+        dp[j] = [dp[j - 1], dp[j], leftup].min + 1
+      end
+      leftup = temp # 更新为下一轮的 dp[i-1, j-1]
+    end
+  end
+  dp[m]
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  s = 'bag'
+  t = 'pack'
+  n, m = s.length, t.length
+
+  # 暴力搜索
+  res = edit_distance_dfs(s, t, n, m)
+  puts "将 #{s} 更改为 #{t} 最少需要编辑 #{res} 步"
+
+  # 记忆化搜索
+  mem = Array.new(n + 1) { Array.new(m + 1, -1) }
+  res = edit_distance_dfs_mem(s, t, mem, n, m)
+  puts "将 #{s} 更改为 #{t} 最少需要编辑 #{res} 步"
+
+  # 动态规划
+  res = edit_distance_dp(s, t)
+  puts "将 #{s} 更改为 #{t} 最少需要编辑 #{res} 步"
+
+  # 空间优化后的动态规划
+  res = edit_distance_dp_comp(s, t)
+  puts "将 #{s} 更改为 #{t} 最少需要编辑 #{res} 步"
+end
diff --git a/codes/ruby/chapter_dynamic_programming/knapsack.rb b/codes/ruby/chapter_dynamic_programming/knapsack.rb
new file mode 100644
index 000000000..c776e7d59
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/knapsack.rb
@@ -0,0 +1,99 @@
+=begin
+File: knapsack.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### 0-1 背包：暴力搜索 ###
+def knapsack_dfs(wgt, val, i, c)
+  # 若已选完所有物品或背包无剩余容量，则返回价值 0
+  return 0 if i == 0 || c == 0
+  # 若超过背包容量，则只能选择不放入背包
+  return knapsack_dfs(wgt, val, i - 1, c) if wgt[i - 1] > c
+  # 计算不放入和放入物品 i 的最大价值
+  no = knapsack_dfs(wgt, val, i - 1, c)
+  yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]
+  # 返回两种方案中价值更大的那一个
+  [no, yes].max
+end
+
+### 0-1 背包：记忆化搜索 ###
+def knapsack_dfs_mem(wgt, val, mem, i, c)
+  # 若已选完所有物品或背包无剩余容量，则返回价值 0
+  return 0 if i == 0 || c == 0
+  # 若已有记录，则直接返回
+  return mem[i][c] if mem[i][c] != -1
+  # 若超过背包容量，则只能选择不放入背包
+  return knapsack_dfs_mem(wgt, val, mem, i - 1, c) if wgt[i - 1] > c
+  # 计算不放入和放入物品 i 的最大价值
+  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]
+  # 记录并返回两种方案中价值更大的那一个
+  mem[i][c] = [no, yes].max
+end
+
+### 0-1 背包：动态规划 ###
+def 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 - 1][c - wgt[i - 1]] + val[i - 1]].max
+      end
+    end
+  end
+  dp[n][cap]
+end
+
+### 0-1 背包：空间优化后的动态规划 ###
+def 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)
+    # 倒序遍历
+    for c in cap.downto(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
+
+### Driver Code ###
+if __FILE__ == $0
+  wgt = [10, 20, 30, 40, 50]
+  val = [50, 120, 150, 210, 240]
+  cap = 50
+  n = wgt.length
+
+  # 暴力搜索
+  res = knapsack_dfs(wgt, val, n, cap)
+  puts "不超过背包容量的最大物品价值为 #{res}"
+
+  # 记忆化搜索
+  mem = Array.new(n + 1) { Array.new(cap + 1, -1) }
+  res = knapsack_dfs_mem(wgt, val, mem, n, cap)
+  puts "不超过背包容量的最大物品价值为 #{res}"
+
+  # 动态规划
+  res = knapsack_dp(wgt, val, cap)
+  puts "不超过背包容量的最大物品价值为 #{res}"
+
+  # 空间优化后的动态规划
+  res = knapsack_dp_comp(wgt, val, cap)
+  puts "不超过背包容量的最大物品价值为 #{res}"
+end
diff --git a/codes/ruby/chapter_dynamic_programming/min_cost_climbing_stairs_dp.rb b/codes/ruby/chapter_dynamic_programming/min_cost_climbing_stairs_dp.rb
new file mode 100644
index 000000000..f570d2e7b
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/min_cost_climbing_stairs_dp.rb
@@ -0,0 +1,39 @@
+=begin
+File: min_cost_climbing_stairs_dp.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### 爬楼梯最小代价：动态规划 ###
+def min_cost_climbing_stairs_dp(cost)
+  n = cost.length - 1
+  return cost[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] = cost[1], cost[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]].min + cost[i] }
+  dp[n]
+end
+
+# 爬楼梯最小代价：空间优化后的动态规划
+def min_cost_climbing_stairs_dp_comp(cost)
+  n = cost.length - 1
+  return cost[n] if n == 1 || n == 2
+  a, b = cost[1], cost[2]
+  (3...(n + 1)).each { |i| a, b = b, [a, b].min + cost[i] }
+  b
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  cost = [0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1]
+  puts "输入楼梯的代价列表为 #{cost}"
+
+  res = min_cost_climbing_stairs_dp(cost)
+  puts "爬完楼梯的最低代价为 #{res}"
+
+  res = min_cost_climbing_stairs_dp_comp(cost)
+  puts "爬完楼梯的最低代价为 #{res}"
+end
diff --git a/codes/ruby/chapter_dynamic_programming/min_path_sum.rb b/codes/ruby/chapter_dynamic_programming/min_path_sum.rb
new file mode 100644
index 000000000..a18fc7b16
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/min_path_sum.rb
@@ -0,0 +1,93 @@
+=begin
+File: min_path_sum.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### 最小路径和：暴力搜索 ###
+def min_path_sum_dfs(grid, i, j)
+  # 若为左上角单元格，则终止搜索
+  return grid[i][j] if i == 0 && j == 0
+  # 若行列索引越界，则返回 +∞ 代价
+  return Float::INFINITY if i < 0 || j < 0
+  # 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价
+  up = min_path_sum_dfs(grid, i - 1, j)
+  left = min_path_sum_dfs(grid, i, j - 1)
+  # 返回从左上角到 (i, j) 的最小路径代价
+  [left, up].min + grid[i][j]
+end
+
+### 最小路径和：记忆化搜索 ###
+def min_path_sum_dfs_mem(grid, mem, i, j)
+  # 若为左上角单元格，则终止搜索
+  return grid[0][0] if i == 0 && j == 0
+  # 若行列索引越界，则返回 +∞ 代价
+  return Float::INFINITY if i < 0 || j < 0
+  # 若已有记录，则直接返回
+  return mem[i][j] if mem[i][j] != -1
+  # 左边和上边单元格的最小路径代价
+  up = min_path_sum_dfs_mem(grid, mem, i - 1, j)
+  left = min_path_sum_dfs_mem(grid, mem, i, j - 1)
+  # 记录并返回左上角到 (i, j) 的最小路径代价
+  mem[i][j] = [left, up].min + grid[i][j]
+end
+
+### 最小路径和：动态规划 ###
+def min_path_sum_dp(grid)
+  n, m = grid.length, grid.first.length
+  # 初始化 dp 表
+  dp = Array.new(n) { Array.new(m, 0) }
+  dp[0][0] = grid[0][0]
+  # 状态转移：首行
+  (1...m).each { |j| dp[0][j] = dp[0][j - 1] + grid[0][j] }
+  # 状态转移：首列
+  (1...n).each { |i| dp[i][0] = dp[i - 1][0] + grid[i][0] }
+  # 状态转移：其余行和列
+  for i in 1...n
+    for j in 1...m
+      dp[i][j] = [dp[i][j - 1], dp[i - 1][j]].min + grid[i][j]
+    end
+  end
+  dp[n -1][m -1]
+end
+
+### 最小路径和：空间优化后的动态规划 ###
+def min_path_sum_dp_comp(grid)
+  n, m = grid.length, grid.first.length
+  # 初始化 dp 表
+  dp = Array.new(m, 0)
+  # 状态转移：首行
+  dp[0] = grid[0][0]
+  (1...m).each { |j| dp[j] = dp[j - 1] + grid[0][j] }
+  # 状态转移：其余行
+  for i in 1...n
+    # 状态转移：首列
+    dp[0] = dp[0] + grid[i][0]
+    # 状态转移：其余列
+    (1...m).each { |j| dp[j] = [dp[j - 1], dp[j]].min + grid[i][j] }
+  end
+  dp[m - 1]
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  grid = [[1, 3, 1, 5], [2, 2, 4, 2], [5, 3, 2, 1], [4, 3, 5, 2]]
+  n, m = grid.length, grid.first.length
+
+  # 暴力搜索
+  res = min_path_sum_dfs(grid, n - 1, m - 1)
+  puts "从左上角到右下角的做小路径和为 #{res}"
+
+  # 记忆化搜索
+  mem = Array.new(n) { Array.new(m, - 1) }
+  res = min_path_sum_dfs_mem(grid, mem, n - 1, m -1)
+  puts "从左上角到右下角的做小路径和为 #{res}"
+
+  # 动态规划
+  res = min_path_sum_dp(grid)
+  puts "从左上角到右下角的做小路径和为 #{res}"
+
+  # 空间优化后的动态规划
+  res = min_path_sum_dp_comp(grid)
+  puts "从左上角到右下角的做小路径和为 #{res}"
+end
diff --git a/codes/ruby/chapter_dynamic_programming/unbounded_knapsack.rb b/codes/ruby/chapter_dynamic_programming/unbounded_knapsack.rb
new file mode 100644
index 000000000..f3d5534f0
--- /dev/null
+++ b/codes/ruby/chapter_dynamic_programming/unbounded_knapsack.rb
@@ -0,0 +1,61 @@
+=begin
+File: unbounded_knapsack.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### 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
+
+### Driver Code ###
+if __FILE__ == $0
+  wgt = [1, 2, 3]
+  val = [5, 11, 15]
+  cap = 4
+
+  # 动态规划
+  res = unbounded_knapsack_dp(wgt, val, cap)
+  puts "不超过背包容量的最大物品价值为 #{res}"
+
+  # 空间优化后的动态规划
+  res = unbounded_knapsack_dp_comp(wgt, val, cap)
+  puts "不超过背包容量的最大物品价值为 #{res}"
+end