LeetCode #188: Best Time to Buy and Sell Stock IV

Problem Statement

(Source) 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).

Analysis

dp[i][j]

: the maximum profit can be achieved in the previous

j

days with at most

i

transactions.

Time Complexity: O(kn2)

Space Complexity: O(kn)

Tags:

Dynamic Programming

.

Solution

class Solution(object):
def maxProfit(self, k, prices):
"""
:type k: int
:type prices: List[int]
:rtype: int
"""
if k <= 0 or (not prices) or len(prices) < 2:
return 0

n = len(prices)
res = 0

if k >= (n >> 1): # Arbitray transactions allowed in this case.
dp = [0 for i in xrange(n + 1)]
for i in xrange(2, n + 1):
dp[i] = dp[i - 1]
j = i - 1
while j > 0 and prices[i-1] > prices[j-1]:
dp[i] = max(dp[i], dp[j-1] + prices[i-1] - prices[j-1])
j -= 1
return dp[-1]

dp = [[0 for j in xrange(n)] for i in xrange(k + 1)]
for i in xrange(1, k + 1):
for j in xrange(1, n):
dp[i][j] = dp[i][j-1]
# Buy at day t and sell at day j.
t = j - 1
while t >= 0 and prices[t] < prices[j]:
profit = max(prices[j] - prices[t], 0)
if t - 1 > 0:
profit += dp[i-1][t-1]
dp[i][j] = max(dp[i][j], profit)
t -= 1
res = max(res, dp[i][j])
return res