Element-wise Arithmetic and Broadcasting Practice Problem

This data science coding problem helps you practice Mathematical & Statistical Operations, element-wise arithmetic and broadcasting, and implementation skills. Read the problem statement, write your solution, and strengthen your understanding of Mathematical & Statistical Operations.

• Problem ID: 55
• Problem key: 55-element-wise-arithmetic-and-broadcasting
• URL: https://datacrack.app/solve/55-element-wise-arithmetic-and-broadcasting
• Difficulty: easy
• Topic: Mathematical & Statistical Operations
• Module: NumPy Foundations

Problem Statement

# 🧩 Element-wise Arithmetic and Broadcasting

---

### 🎯 Goal
NumPy's most powerful feature is **vectorized operations** — applying math to entire arrays without loops. **Broadcasting** extends this to arrays of different shapes. This problem builds your intuition for both, which is essential for every ML implementation.

---

### 🔍 Element-wise vs Broadcasting

**Element-wise** (same shape):
```python
a = np.array([1, 2, 3])
b = np.array([10, 20, 30])
a + b   # → [11, 22, 33]  — adds pairwise
```

**Broadcasting** (different shapes — scalar or compatible array):
```python
a = np.array([1, 2, 3])
a * 3   # → [3, 6, 9]     — scalar broadcast to every element

M = np.array([[1,2,3],[4,5,6]])
M + 10  # → [[11,12,13],[14,15,16]]  — scalar broadcast to all
```

---

### 💻 Task
Implement `array_arithmetic(a, b=None, scalar=None, operation=None)` dispatching to the right NumPy operation.

---

### 📥 Input
- `a`, `b`: lists of numbers (same length for element-wise ops)
- `scalar`: a number (for scalar operations)
- `operation`: string — `"add"`, `"divide"`, `"multiply_scalar"`, `"add_scalar"`, `"power"`

### 📤 Output
- Result array as a Python list

---

### 🧩 Starter Code
```python
import numpy as np

def array_arithmetic(a, b=None, scalar=None, operation=None):
    """
    Perform element-wise or broadcasting arithmetic on NumPy arrays.

    Args:
        a (list): First array
        b (list): Second array (for element-wise ops)
        scalar (number): Scalar value (for broadcasting ops)
        operation (str): The operation to perform

    Returns:
        list: Result as a Python list
    """
    arr_a = np.array(a)

    # 🧠 TODO:
        pass
```

---

### 🔑 Key Concepts
- NumPy operators (`+`, `-`, `*`, `/`, `**`) work element-wise on arrays
- A scalar is automatically broadcast to every element
- No loops needed — NumPy handles iteration internally in optimized C code

Starter Code

import numpy as np

def array_arithmetic(a, b=None, scalar=None, operation=None):
    """
    Perform element-wise or broadcasting arithmetic on NumPy arrays.

    Args:
        a (list): First array
        b (list): Second array (for element-wise ops)
        scalar (number): Scalar value (for broadcasting ops)
        operation (str): The operation to perform

    Returns:
        list: Result as a Python list
    """
    arr_a = np.array(a)

    # 🧠 TODO:
        pass