problem0375

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375. Guess Number Higher or Lower II

题目

We are playing the Guess Game. The game is as follows:

I pick a number from 1 to n. You have to guess which number I picked.

Every time you guess wrong, I'll tell you whether the number I picked is higher or lower.

However, when you guess a particular number x, and you guess wrong, you pay $x. You win the game when you guess the number I picked.

Example:

n = 10, I pick 8.

First round :  You guess 5, I tell you that it's higher. You pay $5.
Second round:  You guess 7, I tell you that it's higher. You pay $7.
Third round :  You guess 9, I tell you that it's lower. You pay $9.

Game over. 8 is the number I picked.

You end up paying $5 + $7 + $9 = $21.

Given a particular n ≥ 1, find out how much money you need to have to guarantee a win.

Credits:Special thanks to @agave and @StefanPochmann for adding this problem and creating all test cases.

解题思路

见程序注释