# GeetCode Hub

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:

```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`

class Solution { public int getMoneyAmount(int n) { } }
Medium
Medium
Medium