Preparing for a data scientist interview at Lyft (or similar top tech companies) means tackling technical challenges that test both your theoretical understanding and practical problem-solving skills. In this article, we’ll solve and explain several data science interview questions—ranging from algorithmic coding to critical concepts in machine learning interpretability and natural language processing. Each question is not only solved, but the underlying concepts are clearly explained, helping you prepare for your next big interview.

Data Science Interview Questions - Lyft

1. Find the Missing Integer Between Two Nearly Identical Lists

Problem Statement

You are given two lists, X and Y. Both lists contain integers in the range [-1000, 1000], and they are identical except that one integer present in X has been removed from Y. Write a function that finds and returns the integer that was removed, doing so in O(1) time and O(n) space. You may not use Python’s set function.

Concepts Involved

• Algorithmic efficiency (Time and Space Complexity)
• Properties of arithmetic and bitwise operations
• Hashing or simple traversal

Optimal Solution Explanation

To achieve O(1) time, we need a solution that doesn’t depend on traversing the list more than once or using nested loops. While hash tables can solve this in O(n) time and space, the problem asks for O(1) time. The trick is to use a mathematical property:

• Summation: Since the only difference between the lists is one missing integer, the sum of X will be greater than the sum of Y by exactly that missing integer.
• XOR Operation: XOR-ing all elements in both lists together will cancel out matching numbers, leaving only the missing number.

Summation Approach

If we compute the sum of X and subtract the sum of Y, the result is the missing integer.

def find_missing_integer_sum(X, Y):
    return sum(X) - sum(Y)

Both sum(X) and sum(Y) are O(n) operations, and the final subtraction is O(1). Thus, the overall time complexity is O(n), which is the minimum possible since we must look at every element at least once.

XOR Approach

The XOR approach leverages the property that a ^ a = 0 and a ^ 0 = a. By XOR-ing all elements of X and Y together, pairs cancel out, leaving the missing integer.

def find_missing_integer_xor(X, Y):
    missing = 0
    for num in X + Y:
        missing ^= num
    return missing

However, to strictly meet O(n) space and not use more memory, you can iterate through both lists in parallel:

def find_missing_integer_xor(X, Y):
    missing = 0
    for num in X:
        missing ^= num
    for num in Y:
        missing ^= num
    return missing

Why Not Use set?

The set method would be tempting, but it’s explicitly excluded in the problem. Additionally, sum and XOR are more space-efficient.

Key Takeaways

• Summation and XOR are fast, constant-time operations per element.
• These approaches are commonly asked in interviews for their elegance and efficiency.

2. Select a Random Number from a Stream in O(1) Space

Problem Statement

Given a stream of numbers (potentially infinite or too large to store), select a random number from the stream so that every number seen so far has an equal probability of being selected. Do this using O(1) space.

Concepts Involved

• Reservoir Sampling Algorithm
• Probability and uniform randomness
• Streaming algorithms

Reservoir Sampling: The Optimal Solution

The classic solution to this problem is the Reservoir Sampling algorithm. Here’s how it works:

1. Initialize result as None and a counter n = 0.
2. For each incoming number x in the stream, increment n by 1.
3. With probability \( \frac{1}{n} \), replace result with x.
4. After the stream ends (or at any point), result contains a randomly selected number, with each seen number having equal probability.

Mathematical Explanation

For each element at position \( i \) in the stream, the probability it’s kept is:

$$ P(\text{element } i \text{ is chosen}) = \frac{1}{i} \prod_{j=i+1}^{n} \left(1 - \frac{1}{j}\right) = \frac{1}{n} $$

So every element has a uniform chance!

Python Implementation

import random

def select_random_from_stream(stream):
    result = None
    n = 0
    for number in stream:
        n += 1
        if random.randint(1, n) == 1:  # With probability 1/n
            result = number
    return result

Only two variables (result and n) are kept, so space complexity is O(1).

Key Takeaways

• Reservoir sampling is the standard for sampling from a stream, widely used in real-world systems.
• It’s both space and time efficient, and a favorite interview question at Facebook, Lyft, and other top tech companies.

3. Giving a Rejection Reason Without Feature Weights (Model Interpretability)

Problem Statement

Suppose you have a binary classification model (e.g., for loan approval) that must provide each rejected applicant with a reason for rejection. However, you do not have access to the feature weights (e.g., if using a black-box model). How can you provide a reason for each rejected applicant?

Concepts Involved

• Model interpretability and explainability
• Counterfactual analysis
• Feature importance (local explanation)
• Perturbation methods (e.g., LIME, SHAP)

Solution: Local Explanation via Counterfactuals

Even without access to feature weights or coefficients, we can still deduce which features most influenced a particular prediction by observing how the prediction changes when individual features are perturbed. This is central to methods like LIME (Local Interpretable Model-agnostic Explanations) and SHAP (SHapley Additive exPlanations).

Step-by-Step Approach

1. For a given rejected applicant, record all the feature values.
2. For each feature, create a hypothetical applicant by changing only that feature to a more favorable value (e.g., increasing income, reducing debt).
3. Pass these hypothetical applicants through the model and observe if the prediction flips from reject to approve.
4. The feature whose change most increases the probability of acceptance (or flips the decision) is a strong candidate for the "reason for rejection".

Why This Works

This method is called counterfactual reasoning or sensitivity analysis. Even with a black-box model, you can infer local feature importance by seeing which feature, when changed, would have helped the applicant.

Example

In this example, only increasing income changes the decision, so income is the main reason for rejection.

Automating the Process

You can write a wrapper function that, for each feature, creates a modified applicant, queries the model, and ranks the features by their impact.

Other Approaches

• LIME: Perturbs many features at once, fits a local surrogate model (like a linear model) to approximate the black-box decision boundary.
• SHAP: Uses game-theory-based Shapley values to assign "credit" to each feature for the prediction.

Key Takeaways

• You do not need to know model internals to provide actionable reasons for individual predictions.
• Local, counterfactual-based explanations are standard for regulated industries (finance, healthcare).

4. Stemming Words in a Sentence Using a Root Dictionary

Problem Statement

Given a dictionary of root words and a sentence, stem all the words in the sentence so that each word is replaced with the shortest root that forms it (if multiple roots can form the word). If a word cannot be formed from any root, keep it as is.

Concepts Involved

• Stemming and lemmatization in NLP
• Efficient string matching (Trie data structure)
• Greedy algorithms

Efficient Solution: Trie-Based Stemming

The problem requires, for each word, finding the shortest prefix in a dictionary of roots. A Trie (prefix tree) is ideal for this task:

1. Insert all roots into a Trie.
2. For each word in the sentence, traverse the Trie to find the shortest matching root as a prefix.
3. If found, replace the word with this root; otherwise, keep the word as is.

Why Trie?

A Trie allows O(k) lookup per word (where k is the word length), which is much faster than matching every root against every word.

Python Implementation

class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_root = False

def build_trie(roots):
    root_node = TrieNode()
    for root in roots:
        node = root_node
        for char in root:
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.is_root = True
    return root_node

def stem_word(word, trie):
    node = trie
    prefix = ''
    for char in word:
        if char not in node.children:
            break
        node = node.children[char]
        prefix += char
        if node.is_root:
            return prefix
    return word

def stem_sentence(sentence, roots):
    trie = build_trie(roots)
    words = sentence.split()
    return ' '.join([stem_word(word, trie) for word in words])

# Example usage
roots = ["cat", "bat", "rat"]
sentence = "the cattle was rattled by the battery"
print(stem_sentence(sentence, roots))
# Output: 'the cat was rat by the bat'

Explanation

• Each word is replaced with the shortest root that is a prefix of the word.
• If no root matches, the word remains unchanged.

Key Takeaways

• Tries are a powerful data structure for prefix search, commonly used in NLP tasks.
• Stemming simplifies feature spaces and helps downstream machine learning models generalize better.

Conclusion

Data science interviews at companies like Lyft, Facebook, and other tech giants combine algorithmic challenges with real-world machine learning and natural language processing concepts. By understanding and practicing the problems above—including efficient search algorithms, streaming algorithms, model interpretability, and NLP stemming—you’ll be well prepared to succeed in your next interview.

Remember: interviewers care not just about your code, but your ability to clearly explain your reasoning, justify your choices, and relate solutions to broader concepts in data science.

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