add generate_parenthesis backtracking approach

backtracking/generate_paranthesis.rb

@@ -0,0 +1,47 @@
+# Given n pairs of parentheses, write a function to generate all combinations
+# of well-formed parentheses.
+#
+# Example 1:
+#
+# Input: n = 3
+# Output: ["((()))","(()())","(())()","()(())","()()()"]
+# Example 2:
+#
+# Input: n = 1
+# Output: ["()"]
+#
+#
+# Constraints:
+#
+# 1 <= n <= 8
+
+# @param {Integer} n
+# @return {String[]}
+def generate_parenthesis(n)
+  parenthesis = []
+  backtrack(parenthesis, "", 0, 0, n)
+  parenthesis
+end
+
+def backtrack(parenthesis, curr, open, close, max)
+  if curr.length == max * 2
+    parenthesis.push(curr)
+    return
+  end
+
+  if open < max
+    backtrack(parenthesis, curr + "(", open + 1, close, max)
+  end
+
+  if close < open
+    backtrack(parenthesis, curr + ")", open, close + 1, max)
+  end
+end
+
+n = 3
+print(generate_parenthesis(n))
+# Output: ["((()))","(()())","(())()","()(())","()()()"]
+
+n = 1
+print(generate_parenthesis(n))
+# Output: ["()"]