How to Solve Guess Number Higher or Lower I I Problem
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Guess Number Higher or Lower II
We are playing the Guessing Game. The game will work as follows: I pick a number between 1 and n. You guess a number. If you guess the right number, you win the game. If you guess the wrong number, th...
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Understanding the Guess Number Higher or Lower I I Problem
Let's break down this LeetCode problem and understand what makes it challenging in interview settings.
Problem Statement
We are playing the Guessing Game. The game will work as follows: I pick a number between 1 and n. You guess a number. If you guess the right number, you win the game. 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. 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.
Guess Number Higher or Lower II
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Examples
n = 10
16
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.
n = 1
0
There is only one possible number, so you can guess 1 and not have to pay anything.
n = 2
1
There are two possible numbers, 1 and 2. - Guess 1. - If this is my number, your total is $0. Otherwise,
Constraints
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