#688 Range Bonus, Point Lookup

A game's leaderboard gives bonus points to ranges of players: "everyone ranked 3 to 9 gets 50 points". Players often check their own bonus total. Write a class BonusBoard:

• new BonusBoard(n) creates players 0 to n - 1 with 0 bonus.
• bonus(left, right, amount) adds amount to every player from left to right, inclusive.
• score(index) returns player index's bonus total.

Both methods should be O(log n).

Each example lists the calls in order, then each call's arguments. The first call creates the object with new BonusBoard(…); the output lists what each call returns (null for the constructor and for methods that return nothing).

Input: ["BonusBoard","bonus","bonus","score","score","score"]
[[6],[1,3,10],[2,5,5],[0],[2],[5]]
Output: [null,null,null,0,15,5]

Input: ["BonusBoard","score"]
[[1],[0]]
Output: [null,0]

Constraints

• 1 <= n <= 10^5
• 0 <= left <= right < n
• -1000 <= amount <= 1000
• At most 10^5 calls.