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

Educative-77 in Java: Accelerate Your Coding Interview Prep

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

# 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:



What is the correct solution to the 1-Queens problem?

What is the correct solution to the 1-Queens problem?

What is the correct solution to the 2-Queens problem?

What is the correct solution to the 2-Queens problem?

What is the correct solution to the 3-Queens problem?

What is the correct solution to the 3-Queens problem?

Is this a valid solution for following?

n = 4

![Image](/udata/nMJrmMMM9W4/s1.png)

Is this a valid solution for following?
n = 4
<img src="/udata/nMJrmMMM9W4/s1.png" alt="Image" />

Can two more queens be added to construct a valid solution, without moving the queens already on the board?

![Image](/udata/4rr2dyvZBaY/s2.png)


Can two more queens be added to construct a valid solution, without moving the queens already on the board?
<img src="/udata/4rr2dyvZBaY/s2.png" alt="Image" />

N-Queens 

N-Queens

# 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 `Solution.java` 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- Edward, please keep in mind that you do not have to print the data of the placeholders. Also, do not mention anything about yourself. \nEdward, you are given the following data in the placeholders: \n- Function name: `totalNQueens` \n- User’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 understand the error using the error’s description, and why the test case failed. You will suggest how the learner 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 `totalNQueens` function(s) and the other function(s) invoked in it/them.  \n-Take your time and review the user’s solution code. \n- Do not review any extra/helper files or functions not invoked in the solution function `totalNQueens`. \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 user to reattempt the problem, to correctly use the coding pattern.

# Review time complexity \n- Please provide a brief time complexity analysis of the function(s) `totalNQueens`.  \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 and in a few lines.

# Review space complexity \n- Please provide a brief space complexity analysis of the function(s) `totalNQueens`.  \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 and in a few lines.

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
        """

        # Helper function to try placing queens row by row
        def backtrack(n, row, diagonals, anti_diagonals, cols):
            if row == n:
                return 1  
        
            solutions = 0  
            
            for col in range(n):
                curr_diagonal = row - col          
                curr_anti_diagonal = row + col     
        
                if (
                    col in cols or
                    curr_diagonal in diagonals or
                    curr_anti_diagonal in anti_diagonals
                ):
                    continue  
                
                cols.add(col)
                diagonals.add(curr_diagonal)
                anti_diagonals.add(curr_anti_diagonal)
        
                solutions += backtrack(n, row + 1, diagonals, anti_diagonals, cols)
        
                cols.remove(col)
                diagonals.remove(curr_diagonal)
                anti_diagonals.remove(curr_anti_diagonal)
        
            return solutions  
                    
        def sol_func(n):
            return backtrack(n, 0, set(), set(), set())

        # store the expected output from the function defined above
        expected = sol_func(self.__inputs[0])
        # store the actual output from the user's solution
        actual = self.__actual_outputs[0]
        
        # multiple outputs will be added at each index respectively for a single test_case
        expected_outputs = []

        # compare the stored expected and user's solution (actual)
        if expected == actual:
            expected_outputs.append(expected)
            self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
        else:
            expected_outputs.append(expected)
            self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

        return self.__edu_result

import java.util.*;

public class Solution {
    public static int totalNQueens(int n) {

        // Replace this placeholder return statement with your code
        return -1;
    }
}

n-queens.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : 3
    output: 
    - 1 : 0

  - name: "testcase 2"
    inputs:
    - 1: 4
    output:
    - 1 : 2

  - name: "testcase 3"
    inputs:
    - 1 : 5
    output: 
    - 1 : 10

  - name: "testcase 4"
    inputs:
    - 1: 6
    output:
    - 1 : 4

  - name: "testcase 5"
    inputs:
    - 1 : 8
    output: 
    - 1 : 92

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 not(1 <= self.__inputs[0] <= 9):
 self.store_result ("Board size is expected to have 1 <= n <= 9", ValidationFunction.FAIL)
 return
 else:
 self.store_result("", ValidationFunction.PASS)

Backtracking

Subsets

Conclusion

N-Queens

Statement

Examples

Understand the problem

Figure it out!

Try it yourself