Orig Description
Problem A
Decimal Sequences
Hanako learned the conjecture that all the non-negative integers appear in the infinite digit sequence of the decimal representation of $\pi$ = 3.14159265..., the ratio of a circle's circumference to its diameter. After that, whenever she watches a sequence of digits, she tries to count up non-negative integers whose decimal representations appear as its subsequences.
For example, given a sequence "3 0 1", she finds representations of five non-negative integers 3, 0, 1, 30 and 301 that appear as its subsequences.
Your job is to write a program that, given a finite sequence of digits, outputs the smallest non-negative integer not appearing in the sequence. In the above example, 0 and 1 appear, but 2 does not. So, 2 should be the answer.
Input
The input consists of a single test case.
$n$
$d_1$ $d_2$ ... $d_n$
$n$ is a positive integer that indicates the number of digits. Each of $d_k$'s $(k = 1, ... , n)$ is a digit. There is a space or a newline between $d_k$ and $d_{k+1}$ $(k = 1, ..., n - 1)$.
You can assume that $1 \leq n \leq 1000$.
Output
Print the smallest non-negative integer not appearing in the sequence.
Sample Input 1
3
3 0 1
Sample Output 1
2
Sample Input 2
11
9 8 7 6 5 4 3 2 1 1 0
Sample Output 2
12
Sample Input 3
10
9 0 8 7 6 5 4 3 2 1
Sample Output 3
10
Sample Input 4
100
3 6 7 5 3 5 6 2 9 1 2 7 0 9 3 6 0 6 2
6 1 8 7 9 2 0 2 3 7 5 9 2 2 8 9 7 3 6
1 2 9 3 1 9 4 7 8 4 5 0 3 6 1 0 6 3 2
0 6 1 5 5 4 7 6 5 6 9 3 7 4 5 2 5 4 7
4 4 3 0 7 8 6 8 8 4 3 1 4 9 2 0 6 8 9
2 6 6 4 9
Sample Output 4
11
Sample Input 5
100
7 2 7 5 4 7 4 4 5 8 1 5 7 7 0 5 6 2 0
4 3 4 1 1 0 6 1 6 6 2 1 7 9 2 4 6 9 3
6 2 8 0 5 9 7 6 3 1 4 9 1 9 1 2 6 4 2
9 7 8 3 9 5 5 2 3 3 8 4 0 6 8 2 5 5 0
6 7 1 8 5 1 4 8 1 3 7 3 3 5 3 0 6 0 6
5 3 2 2 2
Sample Output 5
86
Sample Input 6
1
3
Sample Output 6
0
Extracted Specification
An integer n (1 ≤ n ≤ 1000), representing some quantity or size.
A list of integers d of size n, where each integer is a digit from 0 to 9.
### Example Input:
```
3
3 0 1
```
### Function Signature:
Write a function f(n, d) that takes in the input.
```python
def f(n: int, d: List[int]):
'''
n: an integer
d: a list of integers
'''
```
Test Case Generator
Sure, I can help you write a test case generator for the given problem. Here is a Python function that generates test cases for "Problem A: Decimal Sequences":
```python
import random
def generate_test_case():
# Generate the number of digits, n
n = random.randint(1, 1000)
# Generate a sequence of n digits (each digit is between 0 and 9)
digits = [random.randint(0, 9) for _ in range(n)]
return n, digits
def format_test_case(n, digits):
# Format the test case to match the input format
test_case = f"{n}\n" + " ".join(map(str, digits))
return test_case
# Example usage
for _ in range(5): # Generate 5 example test cases
n, digits = generate_test_case()
test_case = format_test_case(n, digits)
print("Test Case:")
print(test_case)
print()
```
### Explanation:
1. **`generate_test_case()`**:
- It generates a random integer `n` (1 ≤ n ≤ 1000).
- It creates a list of `n` random digits (each digit is between 0 and 9).
2. **`format_test_case(n, digits)`**:
- It formats the generated test case to match the input format specified in the problem statement.
- The formatted test case consists of `n` followed by a newline, and then the `n` digits separated by spaces.
In the **example usage** section, the code generates and prints 5 example test cases. You can adjust the number of test cases by changing the range in the for loop.
Extract Arguments
def extract_arguments(fh):
n = int(fh.readline().strip())
d = list(map(int, fh.read().strip().split()))
return n, d