Best Time to Buy and Sell Stock III

#here we will follow the same strategy like Best time to buy and sell stock II when first buy col=0,first sell col=1, second buy=2, second sell=3 as we are allowed to do 2 buy and 2 sell

def fun(arr,i,k,dp):
    if i==len(arr) or k>=4: #k>=4 means when you used two transaction before reaching to the end of the array.
        return 0
    if dp[i][k]!=-1:
        return dp[i][k]
    if k%2==0: #means buy
        ans=max(-arr[i]+ fun(arr,i+1,k+1,dp), fun(arr,i+1,k,dp) ) #buy or not buy,if buy your net amount will be -ve
    else:
        ans=max(arr[i]+fun(arr,i+1,k+1,dp), fun(arr,i+1,k,dp)) #sell or not sell, if sold you will get share selling amount
    dp[i][k]=ans
    return ans


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