add pascals_triangle in data structure

data_structures/arrays/pascals_triangle.py

@@ -0,0 +1,48 @@
+"""
+Generate Pascal's Triangle.
+
+Reference: https://en.wikipedia.org/wiki/Pascal%27s_triangle
+
+Python doctest can be run with the following command:
+python -m doctest -v pascals_triangle.py
+
+Given a non-negative integer num_rows, generate the first num_rows of Pascal's triangle.
+In Pascal's triangle, each number is the sum of the two numbers directly above it.
+"""
+
+
+class Solution:
+    def generate(self, num_rows: int) -> list[list[int]]:
+        """
+        Generate the first num_rows of Pascal's triangle.
+
+        Args:
+            num_rows (int): The number of rows to generate.
+
+        Returns:
+            list[list[int]]: Pascal's triangle as a list of lists.
+
+        Examples:
+            >>> solution = Solution()
+            >>> solution.generate(5)
+            [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]
+            >>> solution.generate(1)
+            [[1]]
+            >>> solution.generate(0)
+            []
+        """
+        ans: list[list[int]] = []
+        for i in range(num_rows):
+            # Initialize the row with 1s
+            row = [1] * (i + 1)
+            # Compute inner elements by summing elements from the previous row
+            for j in range(1, i):
+                row[j] = ans[i - 1][j - 1] + ans[i - 1][j]
+            ans.append(row)
+        return ans
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()