375. Guess Number Higher or Lower II

• Difficulty: Medium

• Topics: Dynamic Programming, Minimax

• Similar Questions:

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Problem:

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.

Solutions:

class Solution {
public:
    int getMoneyAmount(int n) {
        if (n <= 0)  return 0;
        vector<vector<int>> dp(n + 1, vector<int> (n + 1, 0));

        for (int i = 1; i < n; ++i) {
            dp[i][i+1] = i;
        }

        for (int l = 3; l <= n; ++l) {
            for (int i = 1; i <= n - l + 1; ++i) {
                dp[i][i + l - 1] = INT_MAX;
                for (int mid = i + 1; mid <= i + l - 2; ++mid) {
                    dp[i][i + l - 1] = min(dp[i][i + l -1], max(dp[i][mid - 1], dp[mid+1][i + l - 1]) + mid);
                }
            }
        }

        return dp[1][n];

    }
};