# 24. Pascal Triangle

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/pascal-triangle0652/1)

![](https://badgen.net/badge/Level/Easy/green)

## My Approach

To generate the nth row of Pascal's Triangle, I optimize the simple brute force approach as follows:

* I initialize two vectors, `out` and `prev`, both of size n, with all elements set to 1.
* I iterate through each row, updating the elements of `out` based on the sum of the two corresponding elements from the `prev` vector.
* I also use modular arithmetic to prevent integer overflow.
* In each iteration, I update the `out` array with the values from the `prev` array.

## Explain with Example

For example, let's generate the 5th row of Pascal's Triangle:

```js
- Initialization: out = [1, 1, 1, 1, 1], prev = [1, 1, 1, 1, 1]
- After the first iteration, out = [1, 2, 1, 1, 1], prev = [1, 1, 1, 1, 1]
- After the second iteration, out = [1, 3, 3, 1, 1], prev = [1, 2, 1, 1, 1]
- After the third iteration, out = [1, 4, 6, 4, 1], prev = [1, 3, 3, 1, 1] which is the 5th row of Pascal Triangle.
```

## Time and Auxiliary Space Complexity

* **Time Complexity**: `O(n^2)`, where `n` is the number of rows.
* **Auxiliary Space Complexity**: `O(n)`, as I use two vectors of size `n`.

## Code (C++)

```cpp
class Solution {
public:
    int mod = 1e9 + 7;

    vector<long long> nthRowOfPascalTriangle(int n) {
        vector<long long> out(n, 1), prev(n, 1);
        for (int i = 1; i < n; ++i) {
            for (int j = 1; j < i; ++j) {
                out[j] = (prev[j] + prev[j - 1]) % mod;
            }
            prev = out;
        }
        return out;
    }
};
```

## Contribution and Support

For discussions, questions, or doubts related to this solution, please visit our [discussion section](https://github.com/getlost01/gfg-potd/discussions). We welcome your input and aim to foster a collaborative learning environment.

If you find this solution helpful, consider supporting us by giving a `⭐ star` to the [getlost01/gfg-potd](https://github.com/getlost01/gfg-potd) repository.


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://gl01.gitbook.io/gfg-editorials/2023/11-2023-nov-23/24-pascal-triangle.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.