# 121. Best Time to Buy and Sell Stock

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

```cpp
// Dynamic Programming
int maxProfit(vector<int>& prices) { // time: O(n); space: O(1)
    int res = 0, buy = INT_MAX;
    for (int price : prices) {
        buy = min(buy, price);
        res = max(res, price - buy);
    }
    return res;
}
```

```cpp
// Dynamic Programming
int maxProfit(vector<int>& prices) { // time: O(n); space: O(1)
    int res = 0, buy = INT_MIN;
    for (int price : prices) {
        buy = max(buy, -price);
        res = max(res, price + buy);
    }
    return res;
}
```

```cpp
// Dynamic Programming
int maxProfit(vector<int>& prices) { // time: O(n); space: O(1)
    int res = 0, buy = INT_MIN;
    for (int price : prices) {
        res = max(res, price + buy);
        buy = max(buy, -price);
    }
    return res;
}
```

{% content-ref url="/pages/-LcZ6n2xqhPQ2Q7ok\_6v" %}
[122. Best Time to Buy and Sell Stock II](/practice-of-algorithm-problems/array/122.-best-time-to-buy-and-sell-stock-ii.md)
{% endcontent-ref %}

{% content-ref url="/pages/-LcaryW9cRMBkzf-Imuq" %}
[123. Best Time to Buy and Sell Stock III](/practice-of-algorithm-problems/array/123.-best-time-to-buy-and-sell-stock-iii.md)
{% endcontent-ref %}

{% content-ref url="/pages/-LcavCgzVaLBR3wvx6L4" %}
[188. Best Time to Buy and Sell Stock IV](/practice-of-algorithm-problems/array/188.-best-time-to-buy-and-sell-stock-iv.md)
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{% content-ref url="/pages/-LcdATaC9ECKuxgkzJ-8" %}
[309. Best Time to Buy and Sell Stock with Cooldown](/practice-of-algorithm-problems/array/309.-best-time-to-buy-and-sell-stock-with-cooldown.md)
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{% content-ref url="/pages/-LcdyvMsbxkf5JxGNdhv" %}
[714. Best Time to Buy and Sell Stock with Transaction Fee](/practice-of-algorithm-problems/array/714.-best-time-to-buy-and-sell-stock-with-transaction-fee.md)
{% endcontent-ref %}


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