Dynamic Programming - 375. Guess Number Higher or Lower II

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.

func getMoneyAmount(n int) int {
    var dp = make([][]int, n+1)
    for i := range dp {
        dp[i] = make([]int, n+1)
    }
    
    for j := 2; j <= n; j++ {
        for i := j-1; i > 0; i-- {
            globalMin :=math.MaxInt32
            for k := i+1; k < j; k++ {
                localMax := k + max(dp[i][k-1], dp[k+1][j])
                globalMin = min(globalMin, localMax)
            }
            if i+1 == j {
                dp[i][j] = i 
            } else {
                dp[i][j] = globalMin
            }
        }
    }
    
    return dp[1][n];
}

// recursive dp solution
func getMoneyAmount(n int) int {

    var dp = make([][]int, n+1)
    for i := range dp {
        dp[i] = make([]int, n+1)
    }
    
    return dfs(1, n, &dp)
}


func dfs(start, end int, dp *[][]int) int {
    if start >= end {
        return 0
    }
    if (*dp)[start][end] != 0 {
        return (*dp)[start][end]
    }
    
    res := math.MaxInt32
    for i := start; i <= end; i++ {
        res = min(res, i + max(dfs(start, i - 1, dp), dfs(i + 1, end, dp)))
    }
    
    (*dp)[start][end] = res
    
    return res;
}

func min(i, j int) int {
    if i < j {
        return i
    }
    return j
}

func max(i, j int) int {
    if i > j {
        return i
    }
    return j
}