188. Best Time to Buy and Sell Stock IV Leetcode Python

標籤：dp   python   leetcode   

Say you have an array for which the ith element is the price of a given stock on day i.

Design an algorithm to find the maximum profit. You may complete at most k transactions.

Note:
You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.

Based on Dynamic planning 

maintain two vectors: gpro: to day i the maximum profit

                lpro: to day i the maximum profit with jth sell by day i

the complexity of this problem is O(k*n)

code is as follow:

class Solution:    # @return an integer as the maximum profit     def helper(self, prices):        pro = 0        for i in range(len(prices) - 1):            pro = max(pro, pro + prices[i+1] - prices[i])        return pro    def maxProfit(self, k, prices):        m = len(prices)        if m == 0:            return 0        if k >= m:### if k >=m this problem become best time to sell II            return self.helper(prices)        lpro = [0] * (k + 1)        gpro = [0] * (k + 1)        for i in range(len(prices) - 1):            dif = prices[i + 1] - prices[i]            j = k            while j >= 1:                lpro[j] = max(gpro[j-1]+max(0,dif), lpro[j] + dif)                gpro[j] = max(gpro[j], lpro[j])                j-=1        return gpro[k]

188. Best Time to Buy and Sell Stock IV Leetcode Python