# 118. Pascal's Triangle

# \[A1\] - Brute Force

Time: O(n^2)

Space: O(n^2)

```python
class Solution:
    def generate(self, numRows: int) -> List[List[int]]:
        # Initialize the triangle with the first row
        pascal_triangle = []

        for i in range(numRows):
            # Start each row with a list
            row = [1] * (i + 1)  # Every row starts with 1s

            # Fill in the interior values
            for j in range(1, i):
                row[j] = pascal_triangle[i - 1][j - 1] + pascal_triangle[i - 1][j]

            # Append the completed row to the triangle
            pascal_triangle.append(row)

        return pascal_triangle
```

### **What this code does:**

* Solution **class**: It defines a class that co ntains a method for generating Pascal’s Triangle.
    
* generate **method**: This method takes an integer numRows as input, representing the number of rows in Pascal’s Triangle to generate.
    
* Initializes an empty list called `pascal_triangle` that will hold all rows of Pascal’s Triangle.
    
* Uses a loop to iterate over the range of numRows to generate each row of the triangle.
    
* Each row is initialized with 1s using `[1] * (i + 1)`.
    
* For rows beyond the second, the interior values (non-1s) are calculated using values from the previous row: `pascal_triangle[i - 1][j - 1] + pascal_triangle[i - 1][j]`.
    
* After completing a row, it appends the row to the `pascal_triangle` list.
    
* Finally, the `pascal_triangle` is returned.