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### leetcode Guess Number Higher or Lower II

We are playing the Guess Game. The game is as follows:

I pick a number from 1 to n. You have to guess which number I picked.

Every time you guess wrong, I'll tell you whether the number I picked is higher or lower.

However, when you guess a particular number x, and you guess wrong, you pay $x. You win the game when you guess the number I picked. Example: Given a particular n ≥ 1, find out how much money you need to have to guarantee a win. Hint: 1. The best strategy to play the game is to minimize the maximum loss you could possibly face. Another strategy is to minimize the expected loss. Here, we are interested in the first scenario. 2. Take a small example (n = 3). What do you end up paying in the worst case? 3. Check out this article if you're still stuck. 4. The purely recursive implementation of minimax would be worthless for even a small n. You MUST use dynamic programming. 5. As a follow-up, how would you modify your code to solve the problem of minimizing the expected loss, instead of the worst-case loss? 题意：给定一个数字n，从1~n中选取一个数字y让你猜。在猜的过程中，会告诉你你当前猜的数字x是比y大还是小，猜错的话，需要付$x。给定n,我们最少需要多少的钱来确保我们猜出y呢？

C++

Java

Python

C++ 56ms

Java 14ms

Python 576ms