# 121     Best Time to Buy and Sell Stock

## 121. [Best Time to Buy and Sell Stock](https://leetcode.com/problems/best-time-to-buy-and-sell-stock/description/)

## 1. Question

Say you have an array for which the*i\_thelement 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.
```

## 2. Implementation

**(1) Greedy**

```
class Solution {
    public int maxProfit(int[] prices) {
        if (prices == null || prices.length == 0) {
            return 0;
        }

        int minPrice = prices[0];
        int maxProfit = 0;

        for (int i = 1; i < prices.length; i++) {
            minPrice = Math.min(minPrice, prices[i]);
            maxProfit = Math.max(maxProfit, prices[i] - minPrice);
        }
        return maxProfit;
    }
}
```

## 3. Time & Space Complexity

**Greedy:** 时间复杂度O(n), 空间复杂度O(1)


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