[Leetcode 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.

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

题解：有点饶人的DP。

class Solution {public:    int getMoneyAmount(int n) {  //有点饶人的DP。最小化最大值。最值问题。DP[i][j]代表i~j选出正确值的答案。         vector<vector<int>> dp(n+2,vector<int>(n+2,0));         for(int k=2;k<=n;k++) {             for(int l=1;l+k-1<=n;l++) {                 int r=l+k-1;                 int maxx=INT_MIN;                 dp[l][r]=INT_MAX;                 for(int t=l;t<=r;t++) {                     maxx=max(t+dp[l][t-1],t+dp[t+1][r]);                     dp[l][r]=min(dp[l][r],maxx);                 }             }         }         return dp[1][n];    }};