Check if a string follows a^n b^n pattern or not in Python

The a^n b^n pattern refers to a string that contains exactly n consecutive 'a' characters followed by exactly n consecutive 'b' characters. For example, when n = 3, the string will be "aaabbb".

So, if the input is like s = "aaaaabbbbb", then the output will be True as this follows a^5 b^5 pattern.

Algorithm

To solve this, we will follow these steps −

• Get the size of the string
• Count consecutive 'a' characters from the beginning
• Check if the number of 'a's multiplied by 2 equals the total string length
• Verify that all remaining characters are 'b'
• Return True if both conditions are satisfied

Implementation

Let us see the following implementation to get better understanding −

def solve(s):
    size = len(s)
    
    # Count consecutive 'a' characters from start
    i = 0
    for i in range(size):
        if s[i] != 'a':
            break
    
    # Check if number of 'a's times 2 equals total length
    if i * 2 != size:
        return False
    
    # Check if remaining characters are all 'b'
    for j in range(i, size):
        if s[j] != 'b':
            return False
    
    return True

# Test the function
s = "aaaaabbbbb"
print(solve(s))

True

Testing Multiple Cases

Let's test the function with different examples to verify it works correctly −

def solve(s):
    size = len(s)
    
    # Count consecutive 'a' characters from start
    i = 0
    for i in range(size):
        if s[i] != 'a':
            break
    
    # Check if number of 'a's times 2 equals total length
    if i * 2 != size:
        return False
    
    # Check if remaining characters are all 'b'
    for j in range(i, size):
        if s[j] != 'b':
            return False
    
    return True

# Test cases
test_cases = ["aaabbb", "aabbcc", "ab", "aabb", "aaabb", ""]

for test in test_cases:
    result = solve(test)
    print(f"'{test}' follows a^n b^n pattern: {result}")

'aaabbb' follows a^n b^n pattern: True
'aabbcc' follows a^n b^n pattern: False
'ab' follows a^n b^n pattern: True
'aabb' follows a^n b^n pattern: True
'aaabb' follows a^n b^n pattern: False
'' follows a^n b^n pattern: True

How It Works

The algorithm works by:

• Counting 'a' characters: It counts consecutive 'a' characters from the beginning of the string
• Length validation: For a valid a^n b^n pattern, the total length must be exactly 2n (n 'a's + n 'b's)
• Validating 'b' characters: It ensures all remaining characters after the 'a's are 'b' characters

Conclusion

This solution efficiently checks the a^n b^n pattern by counting consecutive 'a' characters and validating that the remaining half contains only 'b' characters. The time complexity is O(n) where n is the string length.