LC 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.

Runtime: 56 ms, faster than 38.71% of C++ online submissions for Guess Number Higher or Lower II.

Memory Usage: 5.4 MB, less than 0.56% of C++ online submissions for Guess Number Higher or Lower II.

 

class Solution {
  vector<vector<int>>dp;
public:
  int getMoneyAmount(int n) {
    dp.resize(n+1, vector<int>(n+1,0));
    return DP(1,n);  
  }


  int DP(int s, int e) {
    if(s >= e) return 0;
    if(dp[s][e] != 0) return dp[s][e];
    int res = INT32_MAX;
    for(int x=s; x<=e; x++) {
      int tmp = x + max(DP(s,x-1),DP(x+1,e));
      res = min(res, tmp);
    }   
    dp[s][e] = res;
    return res;
  }   
};