Create Arrays with Special Values

1. Background Knowledge

NumPy is Python's foundational library for numerical computing, providing efficient n-dimensional arrays (ndarray) that enable vectorized operations—performing computations on entire arrays without explicit loops. Key functions for this problem:

• np.zeros(shape): Creates array filled with 0.0 (float64 by default).
• np.ones(shape): Creates array filled with 1.0 (float64 by default).
• np.full(shape, fill_value): Creates array filled with any specified value (dtype adapts to value type).

Array shape is a tuple (rows, cols) defining dimensions. Nested lists are Python's native representation: [[0.0, 0.0], [0.0, 0.0]] for 2×2 zeros array. Conversion uses array.tolist().

Prerequisites: Basic NumPy import (import numpy as np), understanding shape tuples, dictionary creation.

2. Algorithm Approach

This is a direct mapping problem: three independent array creation operations stored in a dictionary. No search, sorting, or iteration needed—pure array initialization.

Algorithm:
1. Create zeros array: np.zeros((rows, cols))
2. Create ones array: np.ones((rows, cols))
3. Create fives array: np.full((rows, cols), 5)
4. Convert each to nested list:.tolist()
5. Package in dict: {"zeros": z_list, "ones": o_list, "fives": f_list}

Vectorization principle: NumPy fills entire arrays in contiguous memory using optimized C loops, $O(1)$ initialization regardless of size.

3. Step-by-Step Strategy

import numpy as np

def create_special_arrays(rows, cols):
 # Step 1: Create shape tuple
 shape = (rows, cols)

 # Step 2: Generate arrays using required functions
 zeros_arr = np.zeros(shape) # Shape: (rows, cols), all 0.0
 ones_arr = np.ones(shape) # Shape: (rows, cols), all 1.0
 fives_arr = np.full(shape, 5) # Shape: (rows, cols), all 5