Guess Number Higher or Lower II

Desicription

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:

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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.

Solution

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class Solution {
public:
int getMoneyAmount(int n) {
auto dp = std::vector<std::vector<int>>(n + 1, std::vector<int>(n + 1, 0));
for(int i = 2; i <= n; i++) {
for(int j = i - 1; j >= 1; j--) {
if(j == i - 1) {
dp[j][i] = j;
} else {
int global_min = INT_MAX;
for(int k = j + 1; k < i; k++) {
int local_max = k + std::max(dp[j][k - 1], dp[k + 1][i]);
global_min = std::min(global_min, local_max);
}
dp[j][i] = global_min;
}
}
}

return dp[1][n];
}
};