Problem p03537 - Generation 3

Orig Description

Score : 1000 points
Problem StatementRingo has a string S.
He can perform the following N kinds of operations any number of times in any order.
Operation i: For each of the characters from the L_i-th through the R_i-th characters in S, replace it with its succeeding letter in the English alphabet. (That is, replace a with b, replace b with c and so on.) For z, we assume that its succeeding letter is a.
Ringo loves palindromes and wants to turn S into a palindrome.
Determine whether this is possible.
Constraints
1 \leq |S| \leq 10^5
S consists of lowercase English letters.
1 \leq N \leq 10^5
1 \leq L_i \leq R_i \leq |S|
InputInput is given from Standard Input in the following format:
S
N
L_1 R_1
L_2 R_2
:
L_N R_N
OutputPrint YES if it is possible to turn S into a palindrome; print NO if it is impossible.
Sample Input 1bixzja
2
2 3
3 6
Sample Output 1YES
For example, if we perform Operation 1, 2 and 1 in this order, S changes as bixzja → bjyzja → bjzakb → bkaakb and becomes a palindrome.
Sample Input 2abc
1
2 2
Sample Output 2NO
Sample Input 3cassert
4
1 2
3 4
1 1
2 2
Sample Output 3YES

Extracted Specification

Canonicalized Input Description:

A string S of length between 1 and 100,000 consisting of lowercase English letters.
An integer N (1 ≤ N ≤ 100,000), representing some quantity or number of operations.
N pairs of integers (L_i, R_i) where 1 ≤ L_i ≤ R_i ≤ |S|, indicating some ranges.

### Example Input:

```
bixzja
2
2 3
3 6
```

### Function Signature:
Write a function f(S, N, operations) that takes in the input.
```python
def f(S: str, N: int, operations: List[Tuple[int, int]]):
    '''
    S: a string
    N: an integer
    operations: a list of tuples of integers
    '''
```

Test Case Generator

Certainly! To generate test cases for the given problem, we need to create a string \( S \), an integer \( N \) representing the number of operations, and \( N \) pairs of integers \( (L_i, R_i) \) representing the ranges for each operation. Here is a Python function to generate such test cases:

```python
import random
import string

def generate_test_case():
    # Generate a random length for the string S
    S_length = random.randint(1, 10**5)
    
    # Generate a random string S of lowercase English letters
    S = ''.join(random.choices(string.ascii_lowercase, k=S_length))
    
    # Generate a random number of operations N
    N = random.randint(1, 10**5)
    
    operations = []
    for _ in range(N):
        # Randomly generate L_i and R_i such that 1 <= L_i <= R_i <= |S|
        L_i = random.randint(1, S_length)
        R_i = random.randint(L_i, S_length)
        operations.append((L_i, R_i))
    
    return S, N, operations

def print_test_case():
    S, N, operations = generate_test_case()
    print(S)
    print(N)
    for L, R in operations:
        print(L, R)

# Example usage
print_test_case()
```

This function will generate and print a random test case each time it is called. Here's a breakdown of what each part does:

1. **`S_length`**: Randomly determines the length of the string \( S \) (between 1 and \( 10^5 \)).
2. **`S`**: Generates a random string of lowercase English letters of length `S_length`.
3. **`N`**: Randomly determines the number of operations (between 1 and \( 10^5 \)).
4. **Operations**: For each operation, generate a pair \( (L_i, R_i) \) such that \( 1 \leq L_i \leq R_i \leq |S| \).
5. **`print_test_case`**: This function prints the generated test case in the required format.

You can run the `print_test_case()` function to see how it generates and prints a new random test case each time. This should be helpful for testing your solution to the problem.

Extract Arguments

def extract_arguments(fh):
    S = fh.readline().strip()
    N = int(fh.readline().strip())
    operations = [tuple(map(int, fh.readline().strip().split())) for _ in range(N)]
    return S, N, operations