Total Commas in a Bounded Integer Range

### Problem Write every integer from 1 through `n`, inclusive, in ordinary decimal notation with commas separating groups of three digits from the right. Return the total number of commas used across all those representations. Numbers with fewer than four digits have no commas. For example, 12345 is written `12,345`. ```cpp class Solution { public: int countCommas(int n); }; ``` ### Examples **Example 1:** ```text Input: n = 1000 Output: 1 Explanation: Only the final number is written with a comma: 1,000. ``` **Example 2:** ```text Input: n = 2024 Output: 1025 Explanation: The integers from 1,000 through 2,024 each contain one comma. There are 1025 of them; the earlier integers have none. ``` ### Constraints - `1 <= n <= 100000`. ### Clarifying Questions - Are both 1 and `n` included? Yes. - Are commas counted rather than the numbers themselves? Yes; count every comma used. - Is grouping always by three digits from the right? Yes; no alternative regional grouping is used. - Must the formatted strings be returned? No; return only the total comma count. ### What a Strong Answer Covers - The exact formatting rule and inclusive endpoints. - Correct behavior when no representation contains a comma. - Exact counts at formatting boundaries and at the largest input. - A proof and numeric and resource bounds for this version. ### Follow-up Questions - How would returning every formatted number affect output size? - What would need to be specified if a different grouping convention were allowed? ```hint Use the given upper bound Under this version's bound, a number has either zero or one comma. Identify the first number with a comma, then count how many integers from that point through n are included, or return zero when the range ends earlier. ```