Shape Compatibility Practice Problem

This data science coding problem helps you practice Broadcasting & Vectorization, shape compatibility, and implementation skills. Read the problem statement, write your solution, and strengthen your understanding of Broadcasting & Vectorization.

• Problem ID: 109
• Problem key: 109-shape-compatibility
• URL: https://datacrack.app/solve/109-shape-compatibility
• Difficulty: easy
• Topic: Broadcasting & Vectorization
• Module: NumPy Foundations

Problem Statement

# 🧩 Shape Compatibility

---

### 🎯 Goal
Before two arrays can be broadcast together, their shapes must be **compatible**. This problem teaches you to walk through the broadcasting rules manually — a skill that prevents shape mismatch errors in real NumPy, Pandas, and ML code. You will implement the exact algorithm NumPy uses to determine compatibility and compute the resulting shape.

---

### 🔍 Shape Compatibility

Broadcasting compares shapes **from right to left**.

```python
(5, 1, 3)
(1, 4, 1)
```

| Pair | Result |
|:--|:--|
| `3` and `1` | `3` |
| `1` and `4` | `4` |
| `5` and `1` | `5` |

Final shape:

```python
(5, 4, 3)
```

Rules:

| Pair | Result |
|:--|:--|
| same numbers | keep it |
| one is `1` | use the other |
| different and neither is `1` | incompatible |

---

### 💻 Task
Implement `check_broadcast_compatible(shape_a, shape_b)` that returns the resulting broadcast shape as a list, or `None` if the shapes are incompatible.

---

### 📥 Input
- `shape_a`: list of ints (first array shape)
- `shape_b`: list of ints (second array shape)

### 📤 Output
- List of ints (broadcast result shape), or `None` if incompatible

---

### 🧩 Starter Code
```python
def check_broadcast_compatible(shape_a, shape_b):
    """
    Check if two shapes are broadcast-compatible.

    Args:
        shape_a (list): Shape of the first array
        shape_b (list): Shape of the second array

    Returns:
        list or None: Resulting broadcast shape, or None if incompatible
    """
    # 🧠 TODO: Pad shorter shape with 1s on the left
    # 🧠 TODO: Compare each dimension pair
    # 🧠 TODO: Return result shape or None
    pass
```

---

### 💡 Example
```python
check_broadcast_compatible([3, 4], [4])       # Expected: [3, 4]
check_broadcast_compatible([3, 1], [1, 4])    # Expected: [3, 4]
check_broadcast_compatible([3], [4])           # Expected: None
```

---

### 🔑 Key Concepts
- This is the **exact algorithm** behind `np.broadcast_shapes()` and every NumPy arithmetic operation
- Understanding it prevents the common `ValueError: operands could not be broadcast together` error
- Broadcasting only virtually stretches dimensions of size 1 — it does not physically copy data

Starter Code

def check_broadcast_compatible(shape_a, shape_b):
    """
    Check if two shapes are broadcast-compatible.

    Args:
        shape_a (list): Shape of the first array
        shape_b (list): Shape of the second array

    Returns:
        list or None: Resulting broadcast shape, or None if incompatible
    """
    # 🧠 TODO: Pad shorter shape with 1s on the left
    # 🧠 TODO: Compare each dimension pair
    # 🧠 TODO: Return result shape or None
    pass