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+9+7=21

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

解：

minmax

typedef vector<vector<int>> matrix_int;
class Solution {
public:
int solve(int i,int j,matrix_int &dp)
{
if(i==j)
{
dp[i][j]=0;
return 0;
}
else
{
if(dp[i][j]>0)return dp[i][j];
else
{
int mm=solve(i+1,j,dp)+i;
mm=min(mm,solve(i,j-1,dp)+j);
for(int k=i+1;k<j;++k)
{
int a=solve(i,k-1,dp);
int b=solve(k+1,j,dp);
mm=min(mm,max(a,b)+k);
}
dp[i][j]=mm;
return mm;
}
}
}
int getMoneyAmount(int n) {
matrix_int dp(n+1,vector<int>(n+1,-1));
return solve(1,n,dp);
}
};