Question Definition
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.
Java Solution
public int getMoneyAmount(int n) {
int[][] dp = new int[n + 1][n + 1];
for (int i = 2; i <= n; ++i) {
for (int j = i - 1; j > 0; --j) {
int global_min = Integer.MAX_VALUE;
for (int k = j + 1; k < i; ++k) {
int local_max = k + Math.max(dp[j][k - 1], dp[k + 1][i]);
global_min = Math.min(global_min, local_max);
}
dp[j][i] = j + 1 == i ? j : global_min;
}
}
return dp[1][n];
}
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