Leetcode Guess Number Higher or Lower II problem solution

In this Leetcode Guess Number Higher or Lower II problem solution, We are playing the Guessing Game. The game will work as follows:

I pick a number between 1 and n.

1. You guess a number.
2. If you guess the right number, you win the game.
3. If you guess the wrong number, then I will tell you whether the number I picked is higher or lower, and you will continue guessing.
4. Every time you guess a wrong number x, you will pay x dollars. If you run out of money, you lose the game.

we have given a particular n, return the minimum amount of money you need to guarantee a win regardless of what number I pick.

Problem solution in Python.

class Solution:
    def getMoneyAmount(self, n: int) -> int:
        @lru_cache(maxsize=None)
        def rec(a, b):
            if b < 5:
                return [0, 0, 1, 2, 4][b]
            elif b == a+2:
                return a+1
            else:
                return min(i + max(rec(a,i-1),rec(i+1,b)) for i in range(b-3, a, -4))
        return rec(1, n)

Problem solution in Java.

class Solution {
    public int getMoneyAmount(int n) {
        if(n == 1)
            return 0;
        if(n == 2)
            return 1;
        int dp[][] = new int [n+2][n+2];
        for(int g=0;g<n;g++){
            for(int i=1,j=g+1;j<=n;j++,i++){
                if(g == 0)
                    dp[i][j] = 0;
                else if(g == 1)
                    dp[i][j] = Math.max(i,j);
                else{
                    int min = Integer.MAX_VALUE;
                    for(int k=i;k<j;k++){
                        min = Math.min(min,Math.max(dp[i][k-1]+k,dp[k+1][j]+k));
                    }
                    dp[i][j] = min;
                }
            }
        }
        return dp[1][n];
    }
}

Problem solution in C++.

class Solution {
public:
    vector<vector<int>> storedResults;
    
    int getMoneyAmount(int n) {
        storedResults.clear();
        storedResults.resize(n+2, vector<int>(n+2, -1));
        
        return calc(1, n);
    }
    
    int calc(int low, int high)
    {
        if (low >= high)
        {
            return 0;
        }
        
        int minCost = INT_MAX;
        
        for (int i = (low + high) / 2; i <= high; ++i)
        {
            int rightCost = storedResults[i+1][high];
            if (rightCost == -1)
            {
                rightCost = calc(i+1, high);
                storedResults[i+1][high] = rightCost;
            }
            int leftCost = storedResults[low][i-1];
            if (leftCost == -1)
            {
                leftCost = calc(low, i-1);
                storedResults[low][i-1] = leftCost;
            }
            
            int cost = i + max(rightCost, leftCost);
            minCost = min(cost, minCost);
        }
        
        return minCost;
    }
};

static auto x = [](){
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    return nullptr;
}();