# Python: A very easy solution based on the previous solution. We only need to calculate 3 additional profits and choose the best as the 2nd transaction.

• There are at most 2 transactions:

1. The one that we calculated in the previous problem, which is the biggest profit. We call it "profit1" and its range is [a,b] (a,b are indices of the left bound and right bound).
2. How can we find the 2nd transaction? We only need to consider the following 3 cases:
a. We calculate the biggest profit in prices[:a] (before profit1)
b. We calculate the biggest profit in prices[b+1:] (after profit1)
c. We calculate the biggest price retreat in prices[a:b+1] (inside profit1), which is equivalent to the calculation of biggest profit in prices[a:b+1][::-1] (reversed profit1)

Code is as follows:

``````class Solution(object):
def maxProfit(self, prices):
"""
:type prices: List[int]
:rtype: int
"""
# we need the best profit and its range in prices (the 1st transaction)
profit1, l, r = self.maxProfit_1(prices)

# then we consider other cases where we can make the additional profit (the 2nd transaction)
profits=[]
# we calculate the profit right of the range of "profit1"
profits.append(self.maxProfit_1(prices[r:]))
# we calculate the profit left of the range of "profit1"
profits.append(self.maxProfit_1(prices[:l]))
# we calculate the maximum price retreat(short trade) inside the range of "profit1"
profits.append(self.maxProfit_1(prices[l:r+1][::-1]))
# we choose the biggest among "profits" as the 2nd transaction
profit2=max([profit[0] for profit in profits])

return profit1+profit2

def maxProfit_1(self, prices):
"""
:type prices: List[int]
:rtype: int
"""
# we just need to do a little modification of the last solution
# we use mstart and mend to record the index of the best profit
mstart, bi, b, mend, m = 0, 0, prices[0] if prices else 0, 0, 0
for i,x in enumerate(prices):
if x<b:
b=x
bi=i
if x>b:
if x-b>m:
m=x-b
mstart=bi
mend=i
return m,mstart, mend``````

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