Takeda 2

Set in the turbulent Sengoku period of 16th-century Japan, Takeda 2 is a real-time strategy war game where players assume the role of one of three powerful Daimyo—Takeda Shingen, Oda Nobunaga, or Uesugi Kenshin—each with unique strengths and weaknesses, battling to unite the fragmented nation under their rule. Players must organize armies into formations, command troops in tactical battles while managing morale and fatigue, navigate complex political alliances and marriages, improve characters through experience and special items, and strategically control historically accurate castles and varied terrain on the world map.

To solve this problem, we need to design a time-based key-value store that allows storing multiple values for the same key at different timestamps and retrieving the value of a key at a specific timestamp. The challenge is to efficiently retrieve the most recent value for a key that is less than or equal to the given timestamp.

Approach

1. Data Structure Selection: We use a hash map (dictionary) where each key maps to a list of tuples. Each tuple consists of a timestamp and the corresponding value. The list for each key is maintained in strictly increasing order of timestamps, as per the problem’s constraints.
2. Setting Values: When setting a value for a key, we simply append the (timestamp, value) tuple to the list associated with that key. Since the timestamps are strictly increasing, the list remains sorted without needing explicit sorting.
3. Getting Values: To retrieve the value for a key at a given timestamp:
   • If the key does not exist in the hash map, return an empty string.
   • Otherwise, perform a binary search on the list of (timestamp, value) tuples to find the rightmost tuple where the timestamp is less than or equal to the given timestamp. This is efficiently done using the bisect_left function to find the first tuple with a timestamp greater than the given timestamp, then returning the value of the preceding tuple.

Solution Code

Explanation

• Initialization: The TimeMap class initializes an empty dictionary store to hold key-value pairs along with their timestamps.
• Setting Values: The set method appends a (timestamp, value) tuple to the list corresponding to the key. The list is inherently sorted in increasing order of timestamps due to the problem’s constraint that timestamps are strictly increasing.
• Getting Values: The get method first checks if the key exists in store. If not, it returns an empty string. If the key exists, it performs a binary search using bisect_left to find the position where (timestamp + 1,) would be inserted. The value just before this position (if any) is the most recent value with a timestamp less than or equal to the given timestamp. If no such value exists (i.e., the position is 0), it returns an empty string.

This approach efficiently handles both setting and getting values in logarithmic time relative to the number of timestamps per key, leveraging the sorted nature of the timestamp lists and binary search for optimal performance.