Problem
Say you have an array for which the i-th 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).
Example 1:
Input: [2,4,1], k = 2
Output: 2
Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.
Example 2:
Input: [3,2,6,5,0,3], k = 2
Output: 7
Explanation: Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6-2 = 4.
Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
Notes
See problem 121, 122 and 123.
Note the k. If it is too large(>= n/2), treat it as if with infinitive transactions. We don’t want to loop through a too large k.
Solution
class Solution:
def maxProfit(self, k, prices):
if not prices:
return 0
n = len(prices)
if k >= n//2: # treat it as infinitive transactions
res = 0
for i in range(1, n):
if prices[i] > prices[i-1]:
res += prices[i] - prices[i-1]
return res
buy = [-sys.maxsize] * (k+1)
sell = [0] * (k+1)
for price in prices:
for i in range(1, k+1):
buy[i] = max(buy[i], sell[i-1]-price)
sell[i] = max(sell[i], buy[i]+price)
return sell[-1]