Orig Description
Score : 400 points
Problem StatementWe have a board with a 2 \times N grid.
Snuke covered the board with N dominoes without overlaps.
Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green.
Two dominoes that are adjacent by side should be painted by different colors.
Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
Each domino is represented by a different English letter (lowercase or uppercase).
The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
1 \leq N \leq 52
|S_1| = |S_2| = N
S_1 and S_2 consist of lowercase and uppercase English letters.
S_1 and S_2 represent a valid arrangement of dominoes.
InputInput is given from Standard Input in the following format:
N
S_1
S_2
OutputPrint the number of such ways to paint the dominoes, modulo 1000000007.
Sample Input 13
aab
ccb
Sample Output 16
There are six ways as shown below:
Sample Input 21
Z
Z
Sample Output 23
Note that it is not always necessary to use all the colors.
Sample Input 352
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Sample Output 3958681902
Extracted Specification
An integer N (1 ≤ N ≤ 52), representing some quantity or size.
A string S1 of length N, consisting of lowercase and uppercase English letters.
A string S2 of length N, consisting of lowercase and uppercase English letters.
### Example Input:
```
3
aab
ccb
```
### Function Signature:
Write a function f(N, S1, S2) that takes in the input.
def f(N: int, S1: str, S2: str):
'''
N: an integer
S1: a string
S2: a string
'''
Test Case Generator
Based on the provided problem statement, I'll write a test case generator in Python for the given problem. The test case generator will create random valid inputs for the problem, ensuring it adheres to the constraints provided.
Here's your test case generator:
```python
import random
import string
def generate_domino(N):
"""
Generate a valid arrangement of dominoes for a 2xN grid.
"""
S1 = []
S2 = []
# Generate dominos
i = 0
while i < N:
if i < N - 1 and random.choice([True, False]):
# Place a vertical domino
domino = random.choice(string.ascii_letters)
S1.append(domino)
S2.append(domino)
i += 1
else:
# Place a horizontal domino
domino = random.choice(string.ascii_letters)
S1.append(domino)
S2.append(domino)
if i < N - 1:
S1.append(domino)
S2.append(domino)
i += 1
i += 1
return ''.join(S1[:N]), ''.join(S2[:N])
def tcgen():
N = random.randint(1, 52)
S1, S2 = generate_domino(N)
return N, S1, S2
# Example usage:
N, S1, S2 = tcgen()
print(N)
print(S1)
print(S2)
```
### Explanation:
1. **`generate_domino(N)` Function**:
- This function creates a valid arrangement of dominoes for a 2xN grid.
- It randomly decides whether to place a vertical domino or a horizontal domino.
- Vertical dominos are placed when `random.choice([True, False])` returns `True`. This ensures coverage of both rows at the same column.
- Horizontal dominos are placed in pairs, ensuring that they span two columns in the same row.
- The loop ensures that it doesn't exceed the bounds of the grid.
2. **`tcgen()` Function**:
- Randomly generates the number of columns \( N \).
- Calls `generate_domino(N)` to get valid `S1` and `S2`.
- Returns the generated test case.
### Usage:
- The `tcgen()` function can be called to generate and print a random test case. You can run it multiple times to get diverse sets of inputs.
This approach ensures that the generated test cases are valid according to the problem constraints and models the typical structure of competitive programming test case generators.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
S_1 = fh.readline().strip()
S_2 = fh.readline().strip()
return N, S_1, S_2