Package g0301_0400.s0375_guess_number_higher_or_lower_ii

Class Solution

  • public class Solution
extends Object
    375 - Guess Number Higher or Lower II.

    Medium

    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

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • getMoneyAmount

        public int getMoneyAmount​(int n)