Exercise 2: Generate All Sequences 🔢

Your Task

Write a function all_sequences(n, k) that returns all sequences of length k where each element is chosen from 1 to n. Elements can repeat.

Return the sequences in any order.

---

Examples

print(all_sequences(2, 1))
# Output: [[1], [2]]

print(all_sequences(2, 2))
# Output: [[1, 1], [1, 2], [2, 1], [2, 2]]

print(all_sequences(3, 2))
# Output: [[1,1], [1,2], [1,3], [2,1], [2,2], [2,3], [3,1], [3,2], [3,3]]

---

The Pattern

At each position you loop through all n choices and pick one:

            []
          / | \
        [1] [2] [3]        ← pick first element
        /|\  /|\  /|\
    [1,1][1,2][1,3] ...    ← pick second element

When the sequence reaches length k, add it to the result.

---

Starter Code

def all_sequences(n, k):
    # Your code here
    pass

# Test your function:
print(all_sequences(2, 1))
# Expected: [[1], [2]]

print(all_sequences(2, 2))
# Expected: [[1, 1], [1, 2], [2, 1], [2, 2]]

print(all_sequences(3, 2))
# Expected: [[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]

print(all_sequences(2, 3))
# Expected: [[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,1,1],[2,1,2],[2,2,1],[2,2,2]]

---

Hints