Package g0301_0400.s0375_guess_number_higher_or_lower_ii

Class Solution

java.lang.Object
g0301_0400.s0375_guess_number_higher_or_lower_ii.Solution
public class Solution extends java.lang.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 Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    getMoneyAmount(int n)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • getMoneyAmount

      public int getMoneyAmount(int n)