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.

public class Solution {
    public int getMoneyAmount(int n) {
        int[][] dp = new int[n+1][n+1];
        return solve(dp, 1, n);
    }
    
    int solve(int[][] dp, int lo, int hi){
        if(lo>=hi) return 0;
        if(dp[lo][hi] != 0) return dp[lo][hi];
        dp[lo][hi] = Integer.MAX_VALUE;
        for(int i=lo; i<=hi; i++){
            int temp = i+Math.max(solve(dp, lo, i-1), solve(dp, i+1, hi));
            dp[lo][hi] = Math.min(dp[lo][hi], temp);
        }
        
        return dp[lo][hi];
    }
}

二刷
同上

class Solution {
    public int getMoneyAmount(int n) {
        int[][] dp = new int[n+1][n+1];
        return solve(dp, 1, n);
    }
    
    private int solve(int[][] dp, int lo, int hi){
        if(lo>=hi) return 0;
        if(dp[lo][hi]!=0) return dp[lo][hi];
        dp[lo][hi] = Integer.MAX_VALUE;
        for(int i=lo; i<=hi; i++){
            int temp = i + Math.max(solve(dp, lo, i-1), solve(dp, i+1, hi));
            dp[lo][hi] = Math.min(dp[lo][hi], temp);
        }
        return dp[lo][hi];
    }
}