请完成最优二分检索树的代码

以下是最优二分检索树的 Python 代码：

def optimal_bst(p, q, n):
    e = [[0] * (n + 1) for i in range(n + 1)]
    w = [[0] * (n + 1) for i in range(n + 1)]
    root = [[0] * n for i in range(n)]
    for i in range(n + 1):
        e[i][i - 1] = q[i - 1]
        w[i][i - 1] = q[i - 1]
    for l in range(1, n + 1):
        for i in range(n - l + 1):
            j = i + l - 1
            e[i][j] = float('inf')
            w[i][j] = w[i][j - 1] + p[j] + q[j]
            for r in range(i, j + 1):
                t = e[i][r - 1] + e[r + 1][j] + w[i][j]
                if t < e[i][j]:
                    e[i][j] = t
                    root[i][j - 1] = r
    return e[0][n - 1], root

其中，`p` 和 `q` 分别是节点的概率和虚拟节点的概率，`n` 是节点的数量。返回值是最小期望代价和和根节点数组 `root`。