title
You are given an integer array prices where prices[i] is the price of a given stock on the ith day.
Design an algorithm to find the maximum profit. You may complete at most k transactions.
Notice that you may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).
Example 1:
Input: k = 2, prices = [2,4,1]
Output: 2
Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.
Example 2:
Input: k = 2, prices = [3,2,6,5,0,3]
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.
Constraints:
0 <= k <= 1090 <= prices.length <= 10000 <= prices[i] <= 1000
solution
class Solution:
def maxProfit(self, k: int, prices: List[int]) -> int:
n = len(prices)
# 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]