Check if String Is Decomposable Into Value-Equal Substrings

Here’s the Python solution:

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class Solution:
    def isDecomposable(self, s: str) -> bool:
        n = len(s)
        i = 0
        count2 = 0
        while i < n:
            count = 0
            ch = s[i]
            while i < n and s[i] == ch:
                count += 1
                i += 1
            if count % 3 == 2:
                count2 += 1
            elif count % 3 == 1 or count2 > 1:
                return False
        return count2 == 1

This algorithm works by iterating over the string and counting the number of consecutive characters that are the same. If the count of a group of characters modulo 3 is 2, it increments count2, which tracks the groups of length 2. If the count modulo 3 is 1, or if count2 is more than 1, it returns False, as these cases do not satisfy the conditions. In the end, it checks if count2 is 1, which means it found exactly one group of length 2. If so, it returns True. Otherwise, it returns False.

The use of counters is a key part of this solution. It also demonstrates a few other fundamental programming and problem-solving concepts:

  1. String Traversal: The algorithm walks through the given string, character by character, in order to examine each part of the string. This is a common technique in problems involving strings or arrays.

  2. Grouping: The algorithm identifies groups of the same character by checking if the current character is the same as the last. This kind of operation is common in many string or array problems.

  3. Conditional Logic: The algorithm uses conditions to determine whether the string can be broken up according to the rules. In this case, the conditions are based on the modulo operation and the value of the counter.

  4. State Maintenance: The algorithm maintains a “state” (the current character and count) as it traverses the string, and updates that state as necessary based on what it encounters.

  5. Early Exit: The algorithm returns as soon as it knows the answer, which is a common optimization strategy. This can greatly improve performance for larger inputs.

The following code groups characters by three:

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if i == len(s) or s[i] != s[i - 1]:
    if c % 3 == 1 or c % 3 == 2 and twos:
        return False
    if c % 3 == 2:
        twos += 1
    c = 1
else:
    c += 1

Here’s what they’re doing:

  • The condition if i == len(s) or s[i] != s[i - 1]: checks if the end of the string has been reached, or if the current character is different from the previous one. If either of these conditions are met, the code inside this if block will execute. This marks the end of a group of the same characters.

  • The line if c % 3 == 1 or c % 3 == 2 and twos: checks if the length of the current group (c) is not a multiple of 3 (excluding 2, unless a group of 2 has already been encountered), in which case it returns False.

  • The line if c % 3 == 2: checks if the length of the current group (c) is 2. If so, it increments the twos counter, indicating that a group of length 2 has been found.

  • The line c = 1 resets the counter c for the next group.

  • The line else: c += 1 increments the counter c if the current character is the same as the previous one, continuing the count of the current group.

So, these lines of code handle both the grouping of characters by 3, as well as the special case where one group is allowed to be of length 2.

The code does not explicitly group characters by 2. Instead, it allows one group to have a length of 2 as a special case while counting groups of characters.

The line if c % 3 == 2: inside the if i == len(s) or s[i] != s[i - 1]: block checks if the current group length (c) is 2. If so, it increments the twos counter, indicating that a group of length 2 has been found.

Furthermore, the line if c % 3 == 1 or c % 3 == 2 and twos: ensures that only one group of length 2 is allowed. If a group of length 2 has already been found (twos is not 0) and another group is encountered with length not divisible by 3 (either 1 or 2), the function will return False.

So, while there isn’t a specific section of code dedicated to grouping characters by 2, the ability to handle one group of 2 is integrated within the logic of handling groups of 3.