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

Educative-99 in JavaScript: 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

# Statement

Given an $m \times n$ 2D grid of characters and `word` as a string, we need to determine if the word can be constructed from letters of **sequentially adjacent** cells. The cells are considered sequentially adjacent when they are neighbors to each other either horizontally or vertically. The function should return TRUE if the word can be constructed and FALSE otherwise.

**Constraints:**

- `m` $=$ `board.length`
- `n` $=$ `board[i].length`, where $0 \leq$ `i` $<$ `m`
- $1 \leq$ `m`, `n` $\leq 6$
- $1 \leq$ `word.length` $\leq 15$
- `board` and `word` consist of only lowercase or uppercase English letters.
- The search is not case-sensitive.


# Examples

Can we find the word $magnanimous$ in the given grid?
```text
[['K', 'I', 'C', 'D', 'L', 'J', 'M', 'R']
 ['V', 'M', 'S', 'P', 'C', 'F', 'A', 'G']
 ['C', 'A', 'G', 'D', 'J', 'O', 'L', 'O']
 ['Q', 'Z', 'N', 'T', 'F', 'X', 'C', 'T']
 ['R', 'L', 'A', 'N', 'I', 'R', 'G', 'D']
 ['J', 'A', 'W', 'Y', 'M', 'O', 'U', 'A']
 ['Z', 'A', 'P', 'D', 'R', 'C', 'S', 'D']
 ['Y', 'V', 'A', 'F', 'P', 'L', 'Z', 'T']]
```


Can we find the word <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>a</mi><mi>g</mi><mi>n</mi><mi>a</mi><mi>n</mi><mi>i</mi><mi>m</mi><mi>o</mi><mi>u</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">magnanimous</annotation></semantics></math>magnanimous in the given grid?
<pre><code class="language-text">[['K', 'I', 'C', 'D', 'L', 'J', 'M', 'R']
 ['V', 'M', 'S', 'P', 'C', 'F', 'A', 'G']
 ['C', 'A', 'G', 'D', 'J', 'O', 'L', 'O']
 ['Q', 'Z', 'N', 'T', 'F', 'X', 'C', 'T']
 ['R', 'L', 'A', 'N', 'I', 'R', 'G', 'D']
 ['J', 'A', 'W', 'Y', 'M', 'O', 'U', 'A']
 ['Z', 'A', 'P', 'D', 'R', 'C', 'S', 'D']
 ['Y', 'V', 'A', 'F', 'P', 'L', 'Z', 'T']]
</code></pre>

Can we find the word $callous$ from the given grid?
```text
[['D', 'O', 'C', 'A', 'L']
 ['O', 'J', 'N', 'L', 'Z']
 ['T', 'Z', 'Y', 'L' ,'K']
 ['G', 'Y', 'R', 'O', 'U']
 ['F', 'K', 'M', 'W', 'P']]
```


Can we find the word <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi><mi>o</mi><mi>u</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">callous</annotation></semantics></math>callous from the given grid?
<pre><code class="language-text">[['D', 'O', 'C', 'A', 'L']
 ['O', 'J', 'N', 'L', 'Z']
 ['T', 'Z', 'Y', 'L' ,'K']
 ['G', 'Y', 'R', 'O', 'U']
 ['F', 'K', 'M', 'W', 'P']]
</code></pre>

Word Search

Word Search

## Try it yourself

Implement your solution in the following coding playground.

# Template for backtracking using dfs

class backtracking:
    def __init__(self):
        self.state = []    
        
    def dfs(state):
        res = []
        if is_solution(state):
            res.append(state[:]) # e.g. add a copy of the state to final result list
            return

        for choice in choices:
            if valid(choice):
                state.add(choice) # make move
                dfs(state)
                state.remove(choice) # backtrack

# Template for finding neighbours

class neighbors:
    def __init__(self):
        self.grid = [[]]
        
    def left(grid, row, col):
        return grid[row][col-1]
    
    def right(grid, row, col):
        return grid[row][col+1]
    
    def up(grid, row, col):
        return grid[row-1][col]

    def down(grid, row, col):
        return grid[row+1][col]

    

Help me debug only the function Word Search . . I don't need the corrected code.I don't want explanations or code review. Just provide me the exact and to-the-point error that helps me run the code successfully on the test cases provided.

Please help me understand why this code failed for the last failed test case. Don't give me the corrected code. . If yes, then Just provide me the exact and to-the-point error that helps me run the code successfully on the test cases provided.

Your current task is to review only the wordSearch function and the other function(s) invoked in it/them. Do not review extra/helper files or functions not invoked in the solution function wordSearch. Do not review the code of data structures 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. Also, Answer the following questions: Is the Backtracking pattern used? Take your time and review the code.

Please provide a brief time complexity analysis of the function wordSearch. While calculating time complexity, include the time complexity of built-in Javascript functions invoked by the code. The Answer should be to the point and in a few lines.

Please provide a brief Space complexity analysis of the function wordSearch. While calculating space complexity, include the space complexity of built-in Javascript functions invoked by the code. 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). The Answer should be to the point and in a few lines

TwoDArray

import DataStructure from "../../data/DataStructure.js";

// className: TwoDArray
export default class TwoDArray extends DataStructure {
  constructor() {
    super();
    // class attributes
  }

  // throw parsing errors for incorrect test case format
  onError(data) {
    process.stderr.write("Parsing Error: " + data + " in TwoDArray is not parsable");
    process.exit();
  }

  toString = function () {
    // override print() for your data structure
  };

  // return value will be passed to user program
  construct(value, typeOfArr) {
    // parse test case in json string 'value' to your desired data structure
    return JSON.parse(JSON.stringify(value));
  }

  // input param contains return value of user program
  traverse(input, typeOfArr) {
    // TwoDArray your data structure 'input' to a json string representing a test case output
  }
}


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
 """

 # Function to search a specific word in the grid
 def word_search_eval(grid, word):
 n = len(grid)
 m = len(grid[0])
 for row in range(n):
 for col in range(m):
 if depth_first_search(row, col, word, grid):
 return True
 return False

 # Apply backtracking on every element to search the required word
 def depth_first_search(row, col, word, grid):
 if len(word) == 0:
 return True

 if row < 0 or row == len(grid) or col < 0 or col == len(grid[0]) \
 or grid[row][col].lower() != word[0].lower():
 return False

 grid[row][col] = '*'

 for rowOffset, colOffset in [(0, 1), (1, 0), (0, -1), (-1, 0)]:
 if depth_first_search(row + rowOffset, col + colOffset, word[1:], grid):
 return True

 grid[row][col] = word[0]

 return False
 
 expected = word_search_eval(self.__inputs[0], self.__inputs[1])

 # 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(expected)

 if json.dumps(expected) == json.dumps(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

function wordSearch(grid, word){

    // Replace this placeholder return statement with your code
    return false
}

export {
    wordSearch
}


word search (2).yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [['N', 'W', 'L', 'I', 'M'], 
            ['V', 'I', 'L', 'Q', 'O'], 
            ['O', 'L', 'A', 'T', 'O'], 
            ['R', 'T', 'A', 'I', 'N'], 
            ['O', 'I', 'T', 'N', 'C']]
    - 2 : "LATIN"
    output: 
    - 1 : True
  - name: "testcase 2"
    inputs:
    - 1: [['J', 'D', 'E', 'I', 'Y'], 
            ['G', 'I', 'L', 'M', 'O'], 
            ['Z', 'A', 'I', 'E', 'O'], 
            ['L', 'T', 'B', 'S', 'N'], 
            ['S', 'I', 'T', 'C', 'C']]
    - 2: "AIM"
    output:
    - 1 : False
  - name: "testcase 3"
    inputs:
    - 1 : [['L', 'S', 'T', 'I', 'M'], 
            ['I', 'I', 'L', 'M', 'O'], 
            ['S', 'K', 'I', 'E', 'O'], 
            ['P', 'T', 'A', 'S', 'J'], 
            ['M', 'X', 'T', 'A', 'C']]
    - 2 : "GRAB"
    output: 
    - 1 : False
  - name: "testcase 4"
    inputs:
    - 1: [['C', 'S', 'S', 'A', 'M'], 
            ['O', 'I', 'L', 'L', 'O'], 
            ['O', 'L', 'I', 'T', 'O'], 
            ['R', 'T', 'A', 'S', 'N'], 
            ['S', 'I', 'T', 'A', 'C']]
    - 2: "SALT"
    output:
    - 1 : True
  - name: "testcase 5"
    inputs:
    - 1 : [['H', 'D', 'L', 'I', 'M'], 
            ['R', 'I', 'L', 'Z', 'O'], 
            ['W', 'B', 'A', 'E', 'O'], 
            ['H', 'U', 'K', 'V', 'N'], 
            ['S', 'Y', 'E', 'D', 'C']]
    - 2 : "BAKED"
    output: 
    - 1 : True
  

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

def validate_inputs(self) -> None:
 """
 Validate the board and word based on the given constraints.
 Store the result using self.store_result(error_msg, status).
 return: void
 """
 board = self.__inputs[0]
 word = self.__inputs[1]

 def is_valid_2d_array(arr):
 if not isinstance(arr, list) or not all(isinstance(row, list) for row in arr):
 return False # Not a valid 2D array if it's empty or contains non-list elements

 for row in arr:
 if any(elem is None or isinstance(elem, bool) for elem in row):
 return False # Not a valid 2D array if any element in a row is None
 if not all(isinstance(elem, str) and len(elem) == 1 for elem in row):
 return False
 return True

 def has_invalid_values(board, word):
 invalid_values = {False, True, None}
 if any(value.lower() in invalid_values for row in board for value in row):
 return True
 if any(char.lower() in invalid_values for char in word):
 return True
 return False

 if isinstance(board, bool) or isinstance(word, bool):
 self.store_result("Input should be a valid 2D String array", ValidationFunction.FAIL)
 return

 elif not is_valid_2d_array(board):
 self.store_result("Not a valid 2D String array", ValidationFunction.FAIL)
 return

 elif has_invalid_values(board, word):
 self.store_result("Not a valid 2D String array", ValidationFunction.FAIL)
 return

 elif not (1 <= len(word) <= 15):
 self.store_result("Word length should be in the range 1 <= word.length <= 15", ValidationFunction.FAIL)
 return

 else:
 m = len(board)
 n = len(board[0]) if m > 0 else 0

 if not (1 <= m <= 6 and 1 <= n <= 6):
 self.store_result("Board dimensions should be in the range 1 <= m, n <= 6", ValidationFunction.FAIL)
 return

 elif not all(len(row) == n for row in board):
 self.store_result("Each row in the board should have the same length", ValidationFunction.FAIL)
 return

 elif not all(char.isalpha() and char.isascii() for row in board for char in row):
 self.store_result("Board should consist of only lowercase or uppercase English letters only", ValidationFunction.FAIL)
 return

 elif not all(char.isalpha() and char.isascii() for char in word):
 self.store_result("Word should consist of only lowercase or uppercase English letters only", ValidationFunction.FAIL)
 return

 else:
 self.store_result("", ValidationFunction.PASS)

Backtracking

Subsets

Conclusion

Word Search

Statement

Examples

Understand the problem

Figure it out!

Try it yourself