Borodino: The Science of Winning

Borodino: The Science of Winning is a historical wargame set during Napoleon’s 1812 invasion of Russia, featuring 21 playable missions where players command either French or Russian armies. The game offers both turn-based and real-time tactical modes, complemented by an in-game encyclopedia detailing period-accurate uniforms and armament.

To solve this problem, we need to find the length of the longest substring that contains at most two distinct characters. The solution involves efficiently traversing the string while maintaining a sliding window that meets the condition of having at most two distinct characters.

Approach

1. Sliding Window Technique: We use a sliding window approach where the window is defined by two pointers, left and right. The right pointer expands the window by including new characters, while the left pointer contracts the window when more than two distinct characters are present.
2. Frequency Tracking: A dictionary (or hash map) is used to keep track of the frequency of each character within the current window. This helps in efficiently determining the number of distinct characters.
3. Window Adjustment: Whenever the number of distinct characters exceeds two, the left pointer is moved to the right, reducing the window size from the left. This adjustment continues until the window contains at most two distinct characters again.
4. Max Length Update: After each adjustment, the maximum length of the valid window (substring) is updated if the current window length is greater than the previously recorded maximum.

Solution Code

Explanation

1. Initialization: The left pointer starts at 0, and max_len is initialized to 0. The dictionary freq will store the count of each character in the current window.
2. Expanding the Window: The right pointer iterates over each character in the string. For each character, its count in freq is incremented.
3. Shrinking the Window: If the number of distinct characters (keys in freq) exceeds two, the left pointer is moved to the right. The count of the character at left is decremented, and if it reaches zero, the character is removed from freq.
4. Updating Maximum Length: After ensuring the window contains at most two distinct characters, the length of the current valid window (right - left + 1) is compared with max_len, updating max_len if necessary.
5. Result: After processing all characters, max_len holds the length of the longest substring with at most two distinct characters.

This approach efficiently processes the string in O(n) time, where n is the length of the string, as each character is processed exactly once by both pointers. The space complexity is O(1) since the dictionary holds at most three entries (for two distinct characters and during adjustments).