feat: Add Ruby code - chapter "Backtracking" (#1373)

* [feat] add ruby code - chapter backtracking

* feat: add ruby code block - chapter backtracking

codes/ruby/chapter_backtracking/preorder_traversal_iii_template.rb

@@ -0,0 +1,68 @@
+=begin
+File: preorder_traversal_iii_template.rb
+Created Time: 2024-05-22
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+require_relative '../utils/tree_node'
+require_relative '../utils/print_util'
+
+### 判断当前状态是否为解 ###
+def is_solution?(state)
+  !state.empty? && state.last.val == 7
+end
+
+### 记录解 ###
+def record_solution(state, res)
+  res << state.dup
+end
+
+### 判断在当前状态下，该选择是否合法 ###
+def is_valid?(state, choice)
+  choice && choice.val != 3
+end
+
+### 更新状态 ###
+def make_choice(state, choice)
+  state << choice
+end
+
+### 恢复状态 ###
+def undo_choice(state, choice)
+  state.pop
+end
+
+### 回溯算法：例题三 ###
+def backtrack(state, choices, res)
+  # 检查是否为解
+  record_solution(state, res) if is_solution?(state)
+
+  # 遍历所有选择
+  for choice in choices
+    # 剪枝：检查选择是否合法
+    if is_valid?(state, choice)
+      # 尝试：做出选择，更新状态
+      make_choice(state, choice)
+      # 进行下一轮选择
+      backtrack(state, [choice.left, choice.right], res)
+      # 回退：撤销选择，恢复到之前的状态
+      undo_choice(state, choice)
+    end
+  end
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  root = arr_to_tree([1, 7, 3, 4, 5, 6, 7])
+  puts "\n初始化二叉树"
+  print_tree(root)
+
+  # 回溯算法
+  res = []
+  backtrack([], [root], res)
+
+  puts "\n输出所有根节点到节点 7 的路径，要求路径中不包含值为 3 的节点"
+  for path in res
+    p path.map { |node| node.val }
+  end
+end