Learn and practice the Backtracking and Subsets patterns to solve coding interview problems.

Speedrun the Google Coding Interview: Top Problems in Java

The optimal solution to certain problems requires examining all possibilities. If any possibility is ignored, we are unable to say with mathematical certainty that our solution is optimal. In such situations, we use a technique known as backtracking to exhaustively traverse the entire solution space and collect all the information needed to compute the optimal solution. The Subsets pattern groups together those problems where we need to systematically construct all, or, a mathematically defined subset of all, the possible subsets of a given set. Again, the technique used for the construction of such a set of subsets is, in fact, backtracking.

Go With the Flow

# Statement

For a given number, `n`, generate all combinations of balanced parentheses.

**Constraints:**

* $1 \leq$ `n` $\leq 10$

# Examples

# Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

Which is a valid combination of balanced parentheses when n = 2?

Which is a valid combination of balanced parentheses when n = 2?

Which of the following includes valid balanced parentheses?

Which of the following includes valid balanced parentheses?

Which is a valid combination of balanced parentheses when n = 7?

Select all that apply.

Which is a valid combination of balanced parentheses when n = 7?
Select all that apply.

Generate Parentheses

Generate Parentheses

# Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

# Try it yourself

Implement your solution in the following coding playground:



# Quick Fix\nYou are Edward, a Senior Software Engineer who specializes in coding interview patterns, data structures and algorithms, and is great at debugging issues in code.\n\n- Edward, please keep in mind that you do not have to print the data of the placeholders. Also, do not mention anything about yourself.\n\nEdward, you are given the following data in the placeholders:\n- Function name: `generateCombinations`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `Java`\n\n- Edward, your task is to understand the type of error that is occurring in the coding language provided.\n- Once you've understood the error as per the error’s description, and why the test case failed, you will suggest how the candidate can improve their solution code to fix the error.\n- Edward, you will not give the corrected code, just a hint on what the error tells, and how to fix it.\n- Edward, please limit your response strictly to 100 words. No more words than the limit.

# Review Code\nEdward, your current task is to review the `generateCombinations` function(s) and the other function(s) invoked in it/them.\n\n-Take your time and review the candidate's solution code.\n- Do not review any extra/helper files or functions not invoked in the solution function `generateCombinations`.\n- Do not review the code of data structure objects instantiated like a binary tree, linked list, trie, union find, etc., in the solution functions. Just review the solution/algorithm function of the problem. \n- Also, if the solution code doesn’t use the coding pattern stated above, then please encourage the candidate to reattempt the problem using that pattern corectly.

# Review time complexity\n- Please provide a brief time complexity analysis of the function(s) `generateCombinations`. \n- While calculating time complexity, include the time complexity of built-in Java functions invoked by the code. \n- The answer should be to the point in approximately 60 words.

# Review space complexity\n- Please provide a brief space complexity analysis of the function(s) `generateCombinations`. \n- While calculating space complexity, include the space complexity of built-in Java functions invoked by the code. \n- Do not include the space used for the input parameters and the space used for just returning an output (not used as a scratch space). \n- The answer should be to the point in approximately 60 words.

def evaluate_results(self) -> object:
 """
 self.__inputs is the list of inputs that are passed as input to function
 self.__actual_output is a list of outputs that is produced by the learner's code
 return : self.__edu__result object
 """
 def back_track(n, open_braces_count, close_braces_count, output, result):
 # Base case where count of opening and closing braces is "n"
 if open_braces_count >= n and close_braces_count >= n:
 output_str = str(output)

 replace_str = "[],' "

 for c in replace_str:
 output_str = output_str.replace(c, "")
 result.append(output_str)

 # Case where we can still append opening braces
 if open_braces_count < n:
 output.append('(')
 back_track(n, open_braces_count + 1,
 close_braces_count, output, result)
 output.pop()

 # Case where we append closing braces if the current count
 # of closing braces is less than the count of opening braces
 if close_braces_count < open_braces_count:
 output.append(')')
 back_track(n, open_braces_count,
 close_braces_count + 1, output, result)
 output.pop()


 def generate_combinations(n):
 result = []
 output = []
 back_track(n, 0, 0, output, result)

 return result


 def print_result(result):
 for rs in result:
 print("\t\t ", rs)

 # multiple outputs will be added at each index respectively for a single test_case
 expected_outputs = [] 
 # store the 1st expected output that should be displayed to the user 
 expected_outputs.append(generate_combinations(self.__inputs[0]))

 if json.dumps(generate_combinations(self.__inputs[0])) == json.dumps(sorted(self.__actual_outputs[0])):
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 else:
 self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

 return self.__edu_result

import java.util.*;

public class Main{
 public static ArrayList<String> generateCombinations(int n) {
		
 // Replace this placeholder return statement with your code
 
 ArrayList<String> result = new ArrayList<String>();
		return result;
	}
}

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : 1
    output: 
    - 1 : ["()"]
  - name: "testcase 2"
    inputs:
    - 1: 2
    output:
    - 1 : ["(())", "()()"]
  - name: "testcase 3"
    inputs:
    - 1: 3
    output:
    - 1: ["((()))", "(()())", "(())()", "()(())", "()()()"]
  - name: "testcase 4"
    inputs:
    - 1: 4
    output:
    - 1: ["(((())))", "((()()))", "((())())", "((()))()", "(()(()))", "(()()())", "(()())()", "(())(())", "(())()()", "()((()))", "()(()())", "()(())()", "()()(())", "()()()()"]
  - name: "testcase 5"  
    inputs:
    - 1: 5
    output:
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


def sum(input_1, input_2):
    return input_1+input_2

def validate_inputs(self) -> None:
 """
 self.__inputs is the list of inputs that are passed as input to function
 store the result using the self.store_result(error_msg, status)
 return : void
 """
 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 if self.__inputs[0] < 1:
 self.store_result ("Input should be greater than or equal to 1", ValidationFunction.FAIL)
 elif self.__inputs[0] > 10:
 self.store_result("Input should be less than or equal to 10", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Generate Parentheses problem.

Backtracking

Subsets

Conclusion

Generate Parentheses

Statement

Examples

Understand the problem

Figure it out!

Try it yourself