# Kadane's algorithms to leetcode “121 Best Time to Buy and Sell Stock”

I employed the conventional Kadane's algorithms to solve a maximum subarray problem in leetcode Best Time to Buy and Sell Stock - LeetCode

1. Best Time to Buy and Sell Stock

Say you have an array for which the ith element is the price of a given stock on day i.

If you were only permitted to complete at most one transaction (i.e., buy one and sell one share of the stock), design an algorithm to find the maximum profit.

Note that you cannot sell a stock before you buy one.

Example 1:

Input: [7,1,5,3,6,4]
Output: 5
Explanation: Buy on day 2 (price = 1) and sell on day 5 (price = 6), profit = 6-1 = 5.
Not 7-1 = 6, as selling price needs to be larger than buying price.


Example 2:

Input: [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.


My solution

class Solution:
def maxProfit(self, prices):
"""
:type prices: List[int]
:rtype: int
"""
if not prices:
return 0
local_max = global_max = 0
gains = [prices[i]-prices[i-1] for i in range(1, len(prices))]
for cur in gains:
local_max = max(local_max + cur, cur)
global_max = max(global_max, local_max)
return global_max



Runtime: 64 ms, faster than 14.96% of Python3 online submissions for Best Time to Buy and Sell Stock.

Memory Usage: 14 MB, less than 5.08% of Python3 online submissions for Best Time to Buy and Sell Stock

class Solution:
def maxProfit(self, prices):
"""
:type prices: List[int]
:rtype: int
"""
if not prices:
return 0
loc = glo = 0
for i in range(1, len(prices)):
loc = max(loc+prices[i]-prices[i-1], prices[i]-prices[i-1])
glo = max(glo, loc)
return glo


Runtime: 48 ms, faster than 53.38% of Python3 online submissions for Best Time to Buy and Sell Stock.

Memory Usage: 13.8 MB, less than 5.08% of Python3 online submissions for Best Time to Buy and Sell Stock

TestCase

class MyCase(unittest.TestCase):
def setUp(self):
self.solution = Solution3()

def test_a(self):
prices = [7,1,5,3,6,4]
check = self.solution.maxProfit(prices)

def test_b(self):
prices = [1,2,3,4,5]