P9239 [Lanqiao Cup 2023 NOI Qualifier B] Fill-in-the-Blank Problems

## Task A: Date Counting ### Problem Description Xiao Lan now has an array of length $100$, where each element is a digit from $0$ to $9$. The elements of the array from left to right are as follows: ``` 5 6 8 6 9 1 6 1 2 4 9 1 9 8 2 3 6 4 7 7 5 9 5 0 3 8 7 5 8 1 5 8 6 1 8 3 0 3 7 9 2 7 0 5 8 8 5 7 0 9 9 1 9 4 4 6 8 6 3 3 8 5 1 6 3 4 6 7 0 7 8 2 7 6 8 9 5 6 5 6 1 4 0 1 0 0 9 4 8 0 9 1 2 8 5 0 2 5 3 3 ``` Now he wants to find some subsequences in this array that satisfy the following conditions: 1. The subsequence has length $8$. 2. Following the index order, this subsequence can form a date in `yyyymmdd` format, and this date must be a day in the year 2023, for example $20230902$, $20231223$. Here `yyyy` is the year, `mm` is the month, and `dd` is the day. If the month or day has only one digit, it must be padded with a leading zero. Please help Xiao Lan compute how many **distinct** dates in 2023 can be found under the conditions above. The same date should be counted only once. ### Answer Submission This is a fill-in-the-blank (result-only) problem. You only need to compute the result and submit it. The result is an integer. When submitting, write only this integer; any extra content will cause you to get no score. ## Task B: Entropy of a 01 String ### Problem Description For a 01 string $S=x_{1} x_{2} x_{3} \ldots x_{n}$ of length $n$, the Shannon information entropy is defined as $H(S)=-\sum_{i=1}^{n} p\left(x_{i}\right) \log_{2}\left(p\left(x_{i}\right)\right)$, where $p(0),p(1)$ are the proportions of 0s and 1s in this 01 string. For example, for $S=100$, the entropy is $H(S)=-\frac{1}{3}\log _{2}\left(\frac{1}{3}\right)-\frac{2}{3} \log _{2}\left(\frac{2}{3}\right)-\frac{2}{3} \log _{2}\left(\frac{2}{3}\right)=1.3083$. For a 01 string of length $23333333$, if its entropy is $11625907.5798$, and the number of 0s is less than the number of 1s, then how many times does 0 appear in this 01 string? ### Answer Submission This is a fill-in-the-blank (result-only) problem. You only need to compute the result and submit it. The result is an integer. When submitting, write only this integer; any extra content will cause you to get no score.

The input is a single uppercase letter indicating which task it is.

Output the answer corresponding to the given task letter.

Answer template for reference. ```cpp #include using namespace std; int main() { string ans [] = { "The answer of task A", // Replace the content in double quotes with the answer for task A. "The answer of task B", // Replace the content in double quotes with the answer for task B. }; char T; cin >> T; cout