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

Speedrun the Google Coding Interview: Top Problems in Go

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 a string containing digits from 2 to 9 inclusive, with the possibility of each digit appearing multiple times, return all possible letter combinations that the number could represent. Return the answer in any order.

The illustration below shows the mapping of digits to letters in a telephone dial pad. 
> **Note:** The number $1$ on the telephone dial pad does not correspond to any letter, so the input string only contains digits from $2$ to $9$.

**Constraints:**
* $0 \leq$ `digits.length` $\leq 4$

* `digits[i]` is a digit in the range $[2, 9]$

# 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:

[aw, ax, ay, az, bw, bx, by, bz, cw, cx, cy, cz]

What should be the output if the following digits are given as input?

Digits = 29



What should be the output if the following digits are given as input?
Digits = 29

What should be the output if the following digits are given as input?

Digits = 35

What should be the output if the following digits are given as input?
Digits = 35

What should be the output if the following digits are given as input?

Digits = 8

What should be the output if the following digits are given as input?
Digits = 8

What should be the output if the following digits are given as input?

Digits = 12

What should be the output if the following digits are given as input?
Digits = 12

Letter Combinations of a Phone Number

Letter Combinations of a Phone Number

# 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: `letterCombinations`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `Go`\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 `letterCombinations` 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 `letterCombinations`.\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) `letterCombinations`. \n- While calculating time complexity, include the time complexity of built-in Go 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) `letterCombinations`. \n- While calculating space complexity, include the space complexity of built-in Go 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
        """
        # 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(letter_combinations(self.__inputs[0]))

        if json.dumps(sorted(letter_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
# Use backtrack function to generate all possible combinations
def backtrack(index, path, digits, letters, combinations):
    # If the length of path and digits is same,
    # we have a complete combination
    if len(path) == len(digits):
        s = ""
        s = s.join(path)
        combinations.append(s)
        return  # Backtrack
    # Get the list of letters using the index and digits[index]
    possible_letters = letters[digits[index]]
    if possible_letters:
        for letter in possible_letters:
            # Add the letter to our current path
            path.append(letter)
            # Move on to the next category
            backtrack(index + 1, path, digits, letters, combinations)
            # Backtrack by removing the letter before moving onto the next
            path.pop()


def letter_combinations(digits):
    combinations = []
    
    # If the input is empty, immediately return an empty answer array
    if len(digits) == 0:
        return []

    #  Mapping the digits to their corresponding letters
    digits_mapping = {
        "1": [""],
        "2": ["a", "b", "c"],
        "3": ["d", "e", "f"],
        "4": ["g", "h", "i"],
        "5": ["j", "k", "l"],
        "6": ["m", "n", "o"],
        "7": ["p", "q", "r", "s"],
        "8": ["t", "u", "v"],
        "9": ["w", "x", "y", "z"]}

    # Initiate backtracking with an empty path and starting index of 0

    backtrack(0, [], digits, digits_mapping, combinations)
    return combinations


package main

func letterCombinations(digits string) []string {
    // Replace this placeholder return statement with your code
	return make([]string, 0)
}

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : "2"
    output: 
    - 1 : ['a', 'b', 'c']
  - name: "testcase 2"
    inputs:
    - 1: "73"
    output:
    - 1 : ["pd","pe","pf","qd","qe","qf","rd","re","rf","sd","se","sf"]
  - name: "testcase 3"
    inputs:
    - 1: "426"
    output:
    - 1 : ["gam","gan","gao","gbm","gbn","gbo","gcm","gcn","gco","ham","han","hao","hbm","hbn","hbo","hcm","hcn","hco","iam","ian","iao","ibm","ibn","ibo","icm","icn","ico"]
  - name: "testcase 4"
    inputs:
    - 1: "78"
    output:
    - 1 : ["pt","pu","pv","qt","qu","qv","rt","ru","rv","st","su","sv"]
  - name: "testcase 5"
    inputs:
    - 1: "925"
    output:
    - 1 : ["waj","wak","wal","wbj","wbk","wbl","wcj","wck","wcl","xaj","xak","xal","xbj","xbk","xbl","xcj","xck","xcl","yaj","yak","yal","ybj","ybk","ybl","ycj","yck","ycl","zaj","zak","zal","zbj","zbk","zbl","zcj","zck","zcl"]
  - name: "testcase 6"
    inputs:
    - 1: "39"
    output:
    - 1 : ["dw","dx","dy","dz","ew","ex","ey","ez","fw","fx","fy","fz"]
  - name: "testcase 7"
    inputs:
    - 1: "25"
    output:
    - 1 : ["aj","ak","al","bj","bk","bl","cj","ck","cl"]

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : "2"
    output: 
    - 1 : ['a', 'b', 'c']
  - name: "testcase 2"
    inputs:
    - 1: "73"
    output:
    - 1 : ["pd","pe","pf","qd","qe","qf","rd","re","rf","sd","se","sf"]
  - name: "testcase 3"
    inputs:
    - 1: "426"
    output:
    - 1 : ["gam","gan","gao","gbm","gbn","gbo","gcm","gcn","gco","ham","han","hao","hbm","hbn","hbo","hcm","hcn","hco","iam","ian","iao","ibm","ibn","ibo","icm","icn","ico"]
  - name: "testcase 4"
    inputs:
    - 1: "78"
    output:
    - 1 : ["pt","pu","pv","qt","qu","qv","rt","ru","rv","st","su","sv"]
  - name: "testcase 5"
    inputs:
    - 1: "925"
    output:
    - 1 : ["waj","wak","wal","wbj","wbk","wbl","wcj","wck","wcl","xaj","xak","xal","xbj","xbk","xbl","xcj","xck","xcl","yaj","yak","yal","ybj","ybk","ybl","ycj","yck","ycl","zaj","zak","zal","zbj","zbk","zbl","zcj","zck","zcl"]

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 the function
 store the result using the self.store_result(error_msg, status)
 return: void
 """
 digits=self.__inputs[0]
 min_length=0
 max_length=4
 
 if any(num is None for num in digits):
 self.store_result ("Not a valid test case", ValidationFunction.FAIL) 
 elif any(char not in '23456789' for char in digits):
 self.store_result("Input should contain only digits between 2 to 9", ValidationFunction.FAIL)
 elif len(digits) < min_length or len(digits) > max_length:
 self.store_result("Input length should be between 0 and 4", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Letter Combinations of a Phone Number problem.

Backtracking

Subsets

Conclusion

Letter Combinations of a Phone Number

Statement

Examples

Understand the problem

Figure it out!

Try it yourself