Create pascals_triangle.py

maths/pascals_triangle.py

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+"""/**
+ * Pascal's Triangle is an array of binomial coefficients. It can be used for unwrapping terms like
+ * (a + b)^5.
+ * To construct Pascal's Triangle you add the numbers above the child entry together. Here are the first five rows:
+ *     1
+ *    1 1
+ *   1 2 1
+ *  1 3 3 1
+ * 1 4 6 4 1
+ *
+ * Time Complexity: quadratic (O(n^2)).
+ * @see https://en.wikipedia.org/wiki/Pascal's_triangle
+ */ """
+
+# Importing the numpy library as np for numerical operations
+import numpy as np
+
+def pascal(n: int):
+    """
+    Generate Pascal's triangle up to the n-th row.
+    Parameters:
+    n (int): The number of rows in Pascal's triangle to generate.
+    Returns:
+    np.ndarray: A 2D numpy array containing the first n rows of Pascal's triangle.
+    """
+    # Initialize a 2D numpy array with zeros, with shape (n,n) and integer type
+    pascal_array = np.zeros((n, n), dtype=np.int64)
+    # Set the first column of all rows to 1 (the edge values of Pascal's triangle)
+    pascal_array[:, 0] = 1
+
+    # Fill the pascal_array with the correct values for Pascal's triangle
+    for i in range(1, n):
+        # Each element except the edges is the sum of the two directly above it
+        # pascal_array[i, 1:n] = pascal_array[i-1, 1:n] + pascal_array[i-1, 0:n-1]
+        pascal_array[i,1:i+1] = pascal_array[i-1,1:i+1] + pascal_array[i-1,0:i]
+
+    return pascal_array
+
+def show_pascal(pascal_array):
+    """
+    Print Pascal's triangle in a formatted manner.
+    Parameters:
+    pascal_array (np.ndarray): A 2D numpy array containing Pascal's triangle.
+    """
+    # Get the number of rows and columns (should be equal)
+    n, m = pascal_array.shape[:2]
+    # Ensure the array is square (n == m), as required for Pascal's triangle
+    assert n == m
+
+    # Loop through each row and print the values up to the current row index
+    for i in range(n):
+        for j in range(i + 1):
+            print(pascal_array[i, j], end=" ")
+        print()
+
+# Main execution block
+if __name__ == '__main__':
+    # Display Pascal's triangle for 10 rows
+    show_pascal(pascal(10))