**Solution Explanation** The task is to output exactly what is given on the input. No transformation, no additional characters – the output must be an exact copy of the input. The simplest way to achieve this in C++ is to stream the whole input buffer directly to the output buffer. `std::cin.rdbuf()` gives access to the underlying stream buffer of `std::cin`. Writing this buffer to `std::cout` copies all characters (including newlines, spaces, etc.) unchanged. The program works for any size of input and for any content (text or binary data). --- #### Algorithm 1. Turn off the synchronization between C and C++ streams for speed (optional). 2. Copy the entire input buffer to the output buffer. 3. End. --- #### Correctness Proof We prove that the algorithm outputs exactly the input. *Let `I` be the sequence of all characters read from standard input, and `O` be the sequence of all characters written to standard output by the algorithm.* 1. `std::cin.rdbuf()` returns a pointer to the stream buffer that contains exactly the characters that have been read from the input. Therefore, the stream buffer holds the sequence `I`. 2. The statement `std::cout << std::cin.rdbuf();` writes the entire contents of that buffer to the output stream. Consequently, the sequence written to the output is exactly `I`. 3. No other output is produced by the program. Hence `O = I`. Since `O` equals `I`, the algorithm outputs exactly the input, as required. ∎ --- #### Complexity Analysis Let `n` be the number of characters in the input. The algorithm performs a single linear copy of the input to the output. - **Time complexity:** `O(n)` - **Memory usage:** `O(1)` additional memory (the copy is done directly between the two streams). --- #### Reference Implementation (C++17) ```cpp #include int main() { // Optional: speed up I/O for large data std::ios::sync_with_stdio(false); std::cin.tie(nullptr); // Copy the entire input buffer to the output buffer std::cout << std::cin.rdbuf(); return 0; } ``` This program follows exactly the algorithm proven correct above and is fully compliant with the C++17 standard.