Total Characters in String After Transformations I

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Total Characters in String After Transformations I #1586 Most Asked

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StringsDynamic Programming

You are given a string s and an integer t, representing the number of transformations to perform. In one transformation, every character in s is replaced according to the following rules:

If the character is 'z', replace it with the string "ab".
Otherwise, replace it with the next character in the alphabet. For example, 'a' is replaced with 'b', 'b' is replaced with 'c', and so on.

Return the length of the resulting string after exactly t transformations.

Since the answer may be very large, return it modulo 10⁹ + 7.

Example 1:

Input: s = "abcyy", t = 2

Output: 7

Explanation:

First Transformation (t = 1):
- 'a' becomes 'b'
- 'b' becomes 'c'
- 'c' becomes 'd'
- 'y' becomes 'z'
- 'y' becomes 'z'
- String after the first transformation: "bcdzz"
Second Transformation (t = 2):
- 'b' becomes 'c'
- 'c' becomes 'd'
- 'd' becomes 'e'
- 'z' becomes "ab"
- 'z' becomes "ab"
- String after the second transformation: "cdeabab"
Final Length of the string: The string is "cdeabab", which has 7 characters.

Example 2:

Input: s = "azbk", t = 1

Output: 5

Explanation:

First Transformation (t = 1):
- 'a' becomes 'b'
- 'z' becomes "ab"
- 'b' becomes 'c'
- 'k' becomes 'l'
- String after the first transformation: "babcl"
Final Length of the string: The string is "babcl", which has 5 characters.

Constraints:

1 <= s.length <= 10⁵
s consists only of lowercase English letters.
1 <= t <= 10⁵

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

Can you provide more details on the allowed characters in the input string? For instance, are we limited to ASCII characters, or should we expect Unicode characters?
Is the transformation process deterministic, or is there a chance for variations in the output based on the same input?
What is the expected behavior if the string is null or empty?
Are there any limitations on the number of transformations that might be applied?
Could you provide an example of a transformation to help clarify the process?

Brute Force Solution

Approach

The brute force way to solve this is to try every single possible transformation of the string. This means going through each character in the string and deciding whether or not to perform the transformation on it. Then, for each potential transformation, we measure the length of the string and see if it is the shortest we've encountered.

Here's how the algorithm would work step-by-step:

Start with the original string without applying any transformations.
Then, consider applying the transformation to only the first character.
Next, apply the transformation to only the second character and so on, until only the last character is transformed.
After that, try applying the transformation to the first and second characters, then the first and third, and so on - working through all possible pairs of characters.
Continue this pattern, trying all possible combinations of three characters, then four, and so on, until you try applying the transformation to all characters in the string.
For each of these different possibilities, calculate the length of the resulting string.
Keep track of the shortest string length that you find throughout this whole process.
Once you've tried every single combination of transformations, the shortest string length you recorded is your answer.

Code Implementation

def total_characters_in_string_after_transformations_i_brute_force(input_string):
    number_of_characters = len(input_string)
    minimum_length = number_of_characters

    # Iterate through all possible combinations of transformations
    for i in range(2 ** number_of_characters):
        transformed_string = ""

        # Build the transformed string based on the current combination
        for character_index in range(number_of_characters):
            # Check if the character should be transformed
            if (i >> character_index) & 1:
                # Applying transformation as described in problem
                transformed_string += ""
            else:
                transformed_string += input_string[character_index]

        # Update minimum length if necessary
        current_length = len(transformed_string)

        # Keep track of shortest string length that we've encountered
        if current_length < minimum_length:
            minimum_length = current_length

    return minimum_length

Big(O) Analysis

Time Complexity

O(2^n) – The brute force approach considers all possible subsets of characters to transform. For a string of length n, there are 2^n possible subsets (each character can either be transformed or not). For each subset, we potentially iterate through the entire string to calculate the length after transformations. Since calculating the length takes O(n) time, and we perform this operation for each of the 2^n subsets, the overall time complexity is O(n * 2^n). However, the number of subsets (2^n) dominates the string length computation (n), thus simplifying to O(2^n).

Space Complexity

O(N) – The provided brute force solution explores all possible combinations of transformations, which implicitly involves creating and storing modified strings. In the worst-case scenario, the length of the string might be checked for all 2^N possible combinations, where N is the length of the input string. Each transformed string requires space proportional to N to store, although only one shortest string length is tracked at a time. The dominant space cost is the potential creation of temporary string copies during the transformation process, leading to O(N) auxiliary space.

Optimal Solution

Approach

The most efficient strategy involves recognizing that identical characters next to each other can be simplified. We can significantly reduce the string length by only keeping one instance of a repeated character.

Here's how the algorithm would work step-by-step:

Start with the beginning of the string.
Look at each character in the string one at a time.
If a character is the same as the one immediately before it, ignore it; otherwise, keep it.
Continue until you've checked all the characters in the string.
The final string will only contain characters that are different from the one before them, giving you the total number of distinct characters after the transformation.

Code Implementation

def total_characters_after_transformations(input_string):
    transformed_string = ""
    
    if not input_string:
        return 0

    transformed_string += input_string[0]

    # Iterate through the input string starting from the second character.
    for index in range(1, len(input_string)):

        # Only append the character if it's different from the last one.
        if input_string[index] != transformed_string[-1]:
            transformed_string += input_string[index]

    return len(transformed_string)

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the input string of size n exactly once. In each iteration, it performs a constant-time comparison to the previous character. The dominant operation is the single pass through the string, making the time complexity directly proportional to the length of the string, n.

Space Complexity

O(1) – The algorithm iterates through the input string and compares each character to the previous one. It doesn't use any auxiliary data structures like lists, hash maps, or trees to store intermediate results. The only additional memory used is for a few variables to keep track of the current character and potentially the previous character, which takes constant space regardless of the input string's length, N. Therefore, the space complexity is O(1).

Edge Cases

Case	How to Handle
Null input string	Return 0 or throw an IllegalArgumentException, based on requirements/convention.
Empty input string	Return 0 as there are no characters to transform.
String with only one unique character	Handle based on the transformation rules; may result in the same total characters or a reduced number.
String with no transformations possible based on given rules	Return the original string length as no characters are removed or added.
Maximum-length string (considering memory constraints)	Ensure algorithm has acceptable time and space complexity, potentially using StringBuilder efficiently.
String with unicode characters	Ensure character comparisons and manipulations handle unicode characters correctly (e.g., using code points).
String with special characters or whitespace	Handle whitespace and special characters based on transformation rules; they might be skipped or treated as normal chars.
Very long string where intermediate calculations might cause overflow	Use appropriate data types (e.g., long) to prevent integer overflow during calculations of lengths or counts.

Null input string

How to Handle:

Return 0 or throw an IllegalArgumentException, based on requirements/convention.

Empty input string

How to Handle:

Return 0 as there are no characters to transform.

String with only one unique character

How to Handle:

Handle based on the transformation rules; may result in the same total characters or a reduced number.

String with no transformations possible based on given rules

How to Handle:

Return the original string length as no characters are removed or added.

Maximum-length string (considering memory constraints)

How to Handle:

Ensure algorithm has acceptable time and space complexity, potentially using StringBuilder efficiently.

String with unicode characters

How to Handle:

Ensure character comparisons and manipulations handle unicode characters correctly (e.g., using code points).

String with special characters or whitespace

How to Handle:

Handle whitespace and special characters based on transformation rules; they might be skipped or treated as normal chars.

Very long string where intermediate calculations might cause overflow

How to Handle:

Use appropriate data types (e.g., long) to prevent integer overflow during calculations of lengths or counts.