121. Best Time to Buy and Sell Stock
Description
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
.
Example 1:
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.
Example 2:
Input: prices = [7,6,4,3,1] Output: 0 Explanation: In this case, no transactions are done and the max profit = 0.
Constraints:
1 <= prices.length <= 105
0 <= prices[i] <= 104
Solutions
Solution 1: Enumerate + Maintain the Minimum Value of the Prefix
We can enumerate each element of the array $nums$ as the selling price. Then we need to find a minimum value in front of it as the purchase price to maximize the profit.
Therefore, we use a variable $mi$ to maintain the prefix minimum value of the array $nums$. Then we traverse the array $nums$ and for each element $v$, calculate the difference between it and the minimum value $mi$ in front of it, and update the answer to the maximum of the difference. Then update $mi = min(mi, v)$. Continue to traverse the array $nums$ until the traversal ends.
Finally, return the answer.
The time complexity is $O(n)$, where $n$ is the length of the array $nums$. The space complexity is $O(1)$.
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