375. Guess Number Higher or Lower II

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.

dp[i][j]为从i到j的最小值   dp[i][j]
= min (i<=k<=j) { k + max(dp[i][k-1], dp[k+1][j]) }
public class Solution {
public int getMoneyAmount(int n) {
if(n==1) return 0;
int[][] dp=new int[n+1][n+1];
for(int dis=1;dis<n;dis++){
for(int i=0;i+dis<=n;i++){
dp[i][i+dis]=Integer.MAX_VALUE;
for(int k=i;k<=i+dis;k++){
dp[i][i+dis]=Math.min(dp[i][i+dis],k+Math.max(k-1>=i?dp[i][k-1]:0,k+1<=i+dis?dp[k+1][i+dis]:0));
}
}
}
return dp[1]
;
}
}