# The Pascal Row

> Each number is the sum of two numbers above it.

Canonical URL: <https://datadriven.io/problems/the_pascal_row>

Domain: Python · Difficulty: easy · Seniority: L3

## Problem

Given a 0-indexed row number, return that row of Pascal's triangle as a list. Do NOT generate the full triangle; compute the row directly using the combinatorial identity C(n, k).

## Worked solution and explanation

### Why this problem exists in real interviews

This tests **iterative construction of combinatorial values** without generating the full triangle. It checks whether candidates understand that each element in a Pascal's triangle row can be derived from the previous element using a multiplication formula.

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### Break down the requirements

#### Step 1: Initialize the row with 1

Every row of Pascal's triangle starts with 1.

#### Step 2: Compute subsequent elements using the multiplicative formula

Element k in row n is `row[k-1] * (n - k + 1) / k`. This avoids computing factorials.

#### Step 3: Build the full row

Iterate from position 1 to position n, computing each element from the previous one.

---

### The solution

**Iterative row generation with multiplicative update**

```python
def pascal_row(n):
    row = [1]
    for k in range(1, n + 1):
        val = row[k - 1] * (n - k + 1) // k
        row.append(val)
    return row
```

> **Time and Space Complexity**
>
> **Time:** O(n) for computing n+1 elements.
> 
> **Space:** O(n) for the output row.

> **Interviewers Watch For**
>
> Do you use the multiplicative formula or build the entire triangle? Building the whole triangle is O(n^2) time and space, while the single-row approach is O(n) for both.

> **Common Pitfall**
>
> Using floating-point division instead of integer division. Pascal's triangle values are always integers, so `//` avoids precision issues.

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## Common follow-up questions

- How does this relate to binomial coefficients? _(Tests knowledge that element k in row n is C(n, k).)_
- What if you needed the entire triangle up to row n? _(Tests the iterative row-from-previous-row approach.)_
- What if n were very large (e.g., 10^6)? _(Tests whether integer overflow is a concern (not in Python, but in other languages).)_

## Related

- [All practice problems](https://datadriven.io/problems)
- [Mock interview mode](https://datadriven.io/interview/the_pascal_row)
- [Python Interview Questions](https://datadriven.io/python-interview-questions)
- [Data Engineering Interview Prep Guide](https://datadriven.io/data-engineer-interview-prep)
- [Daily Challenge](https://datadriven.io/daily)

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