title
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 two transactions.
Note: You may not engage in multiple transactions at the same time (i.e., you must sell the stock before you buy again).
Example 1:
Input: prices = [3,3,5,0,0,3,1,4]
Output: 6
Explanation: Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3.
Example 2:
Input: prices = [1,2,3,4,5]
Output: 4
Explanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.
Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are engaging multiple transactions at the same time. You must sell before buying again.
Example 3:
Input: prices = [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.
Example 4:
Input: prices = [1]
Output: 0
Constraints:
1 <= prices.length <= 1050 <= prices[i] <= 105
solution
class Solution:
"""
@param prices: Given an integer array
@return: Maximum profit
"""
def maxProfit(self, prices):
n = len(prices)
K = 2
# corner case
if n == 0:
return 0
# main part
dp = [[0] * n for _ in range(K + 1)]
for i in range(1, K + 1):
max_diff = float('-inf')
for j in range(1, n):
max_diff = max(max_diff, (dp[i - 1][j - 2] if j >= 2 else 0) - prices[j - 1])
dp[i][j] = max(dp[i][j - 1], prices[j] + max_diff)
return dp[K][n - 1]