375. Guess Number Higher or Lower II

375. Guess Number Higher or Lower II

• 題目描述：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.

• 題目大意：猜給定範圍的數字，猜錯了需要付相應的錢，求贏得遊戲所需的最少的錢。

• 思路：http://www.cnblogs.com/grandyang/p/5677550.html

• 代碼

  package DP;
  
  /**
  * @author OovEver
  * 2018/1/8 13:46
  */
  public class LeetCode3752 {
    public static int getMoneyAmount(int n) {
  //        其中dp[i][j]表示從數字i到j之間猜中任意一個數字最少需要花費的錢數
        int[][] dp = new int[n + 1][n + 1];
  //        j代表當前的處理長度
        for(int j=2;j<=n;j++) {
            for(int i=j-1;i>0;i--) {
                int globalMin = Integer.MIN_VALUE;
                for(int k=i+1;k<j;k++) {
                    int localMax =k+ Math.max(dp[i][k - 1], dp[k + 1][j]);
                    globalMin = Math.min(globalMin, localMax);
                }
                dp[i][j] = i + 1 == j ? i : globalMin;
            }
        }
        return dp[1][n];
    }
  }