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# 0375. Guess Number Higher or Lower II

<https://leetcode.com/problems/guess-number-higher-or-lower-ii>

## Description

We are playing the Guessing Game. The game will work as follows:

1. I pick a number between `1` and `n`.
2. You guess a number.
3. If you guess the right number, **you win the game**.
4. If you guess the wrong number, then I will tell you whether the number I picked is **higher or lower**, and you will continue guessing.
5. Every time you guess a wrong number `x`, you will pay `x` dollars. If you run out of money, **you lose the game**.

Given a particular `n`, return *the minimum amount of money you need to **guarantee a win regardless of what number I pick***.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/09/10/graph.png)

```
**Input:** n = 10
**Output:** 16
**Explanation:** The winning strategy is as follows:
- The range is [1,10]. Guess 7.
    - If this is my number, your total is $0. Otherwise, you pay $7.
    - If my number is higher, the range is [8,10]. Guess 9.
        - If this is my number, your total is $7. Otherwise, you pay $9.
        - If my number is higher, it must be 10. Guess 10. Your total is $7 + $9 = $16.
        - If my number is lower, it must be 8. Guess 8. Your total is $7 + $9 = $16.
    - If my number is lower, the range is [1,6]. Guess 3.
        - If this is my number, your total is $7. Otherwise, you pay $3.
        - If my number is higher, the range is [4,6]. Guess 5.
            - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $5.
            - If my number is higher, it must be 6. Guess 6. Your total is $7 + $3 + $5 = $15.
            - If my number is lower, it must be 4. Guess 4. Your total is $7 + $3 + $5 = $15.
        - If my number is lower, the range is [1,2]. Guess 1.
            - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $1.
            - If my number is higher, it must be 2. Guess 2. Your total is $7 + $3 + $1 = $11.
The worst case in all these scenarios is that you pay $16. Hence, you only need $16 to guarantee a win.
```

**Example 2:**

```
**Input:** n = 1
**Output:** 0
**Explanation:** There is only one possible number, so you can guess 1 and not have to pay anything.
```

**Example 3:**

```
**Input:** n = 2
**Output:** 1
**Explanation:** There are two possible numbers, 1 and 2.
- Guess 1.
    - If this is my number, your total is $0. Otherwise, you pay $1.
    - If my number is higher, it must be 2. Guess 2. Your total is $1.
The worst case is that you pay $1.
```

**Constraints:**

* `1 <= n <= 200`

## ac

```java
```