Best Time to Buy and Sell Stock IV

#Same approach like 2 and 3, just now k transaction is allowed so cols =2*k(one for buy and one for sell.)
def fun(arr, i, k, dp):
    if i == len(arr) or k == 0:
        return 0
    if dp[i][k] != -1:
        return dp[i][k]
    # buy
    if k % 2 == 0:
        ans = max( -arr[i] + fun(arr, i + 1, k - 1, dp), fun(arr, i + 1, k, dp))
    # sell
    else:
        ans = max( arr[i] + fun(arr, i + 1, k - 1, dp), fun(arr, i + 1, k, dp))

    dp[i][k] = ans
    return ans

class Solution:
    def maxProfit(self, k: int, prices: List[int]) -> int:
        k = 2 * k
        dp = [[-1] * (k + 1) for _ in range(len(prices))]
        return fun(prices, 0, k, dp)