File: calculate-digit-sum-of-a-string/solution.py

Date: 2026-06-06

Time: 15:29

calculate-digit-sum-of-a-string/solution.py

Purpose

This file solves LeetCode 2243 — Calculate Digit Sum of a String. It owns the single algorithmic responsibility of repeatedly chunking a digit string into groups of size k, replacing each group with the string representation of its digit sum, and iterating until the string is short enough (len(s) <= k).

Key Components

Solution.digitSum(self, s: str, k: int) -> str — The sole method. Contract:

• Input: s is a string of ASCII digit characters; k is a positive integer defining group size.
• Output: The reduced string after all rounds of grouping and summing.
• Mutation: None — s is rebound each iteration, not mutated in place.

Patterns

Iterative reduction loop. The while len(s) > k loop is a classic "reduce until stable" pattern. Each iteration produces a strictly shorter string (since summing digits of a group of k digits yields fewer characters than k for any group whose sum < 10^k), guaranteeing termination.

Generator-expression-based chunking. The inner expression s[i:i + k] for i in range(0, len(s), k) slices the string into consecutive chunks of at most k characters. The last chunk may be shorter than k — Python slicing handles this naturally without bounds checking.

Composition via "".join(...). Each chunk's digit sum is computed inline (sum(int(c) for c in chunk)), converted to string, and the results are joined with no separator. This is idiomatic Python for building a string from transformed segments.

Dependencies

Imports: None — uses only builtins (str, int, sum, range, len).

Imported by: The testsolution.py in this same directory, plus hundreds of other test files across the repo. The "Imported By" list in the prompt is misleading — those other test files import their *own* solution.py, not this one. Only calculate-digit-sum-of-a-string/testsolution.py actually imports this Solution class.

Flow

1. Check if len(s) > k. If not, return s immediately.

2. Slice s into chunks: s[0:k], s[k:2k], ..., s[nk:].

3. For each chunk, sum the integer value of each character.

4. Convert each sum back to a string.

5. Concatenate all stringified sums into the new s.

6. Repeat from step 1.

Example: s = "11111222223", k = 3 → chunks "111", "112", "222", "23" → sums 3, 4, 6, 5 → s = "3465" → chunks "346", "5" → sums 13, 5 → s = "135" → len(s) == 3 == k, return "135".

Invariants

• Termination guarantee: Each round reduces string length because a group of d digits (where d <= k) sums to at most 9*d, whose string representation has at most ceil(log10(9*d + 1)) characters — strictly less than d for d >= 2.
• The while-loop condition len(s) > k means the method is a no-op when the input already satisfies the length constraint.
• Each character in s must be a digit — no validation is performed; non-digit characters would raise ValueError from int(c).

Error Handling

None. The method trusts its inputs per LeetCode's constraints. A non-digit character in s would propagate a ValueError from int(c). A k <= 0 would cause an infinite loop (the string never gets shorter, and range(0, len(s), 0) raises ValueError).

Topics to Explore

• [file] calculate-digit-sum-of-a-string/test_solution.py — See the test cases and edge cases exercised against this solution
• [file] sum-of-digits-of-string-after-convert/solution.py — Related problem: converts characters to digit positions then repeatedly sums digits, similar reduction pattern
• [file] add-digits/solution.py — The "digital root" problem uses the same repeated digit-summing idea but has a O(1) math shortcut
• [function] divide-a-string-into-groups-of-size-k/solution.py:Solution.divideString — Same chunking pattern (s[i:i+k]) applied to string partitioning with padding
• [general] iterative-reduction-convergence — When does repeated digit summing terminate in exactly one round vs. many? The answer depends on the relationship between k and the magnitude of possible sums

Beliefs

• digit-sum-terminates — The while loop always terminates because each iteration produces a string strictly shorter than the previous one, as long as k >= 2 and s contains only digits
• digit-sum-no-validation — The method performs no input validation; non-digit characters raise ValueError and k=0 causes ValueError from range
• digit-sum-last-chunk-short — The final chunk in each round may have fewer than k characters, handled implicitly by Python slice semantics
• digit-sum-pure-function — digitSum has no side effects and depends only on its arguments; it does not modify self or any external state