You are given an array prices where prices[i] is the price of a given stock on the ith day. You want to maximize your profit by choosing a single day to buy one stock and choosing a different day in the future to sell that stock. Return the maximum profit you can achieve from this transaction. If you cannot achieve any profit, return 0.
Input: prices = [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.
Note that buying on day 2 and selling on day 1 is not allowed because you must buy before you sell.
Input: prices = [7,6,4,3,1]
Output: 0
Explanation: In this case, no transactions are done and the max profit = 0.
1 <= prices.length <= 10^5
0 <= prices[i] <= 10^4
For the DP approach, we should track the minimum price and the maximum profit while we traverse the prices array. This solution would have a time complexity of O(N) and space complexity of O(1) where N is the size of prices array.
def maxProfit(prices):
"""
:type prices: List[int]
:rtype: int
:Time Complexity: O(N)
:Space Complexity: O(1)
"""
if not prices:
return 0
max_profit = 0
min_price = prices[0]
for i in range(1, len(prices)):
min_price = min(min_price, prices[i])
max_profit = max(max_profit, prices[i] - min_price)
return max_profit