# JavaScript: Stock Prices Problem

**Problem**: Write a function that takes an array of stock prices and returns the best profit you could make from one purchase and one sale.

For example:

```
const prices = [10, 6, 3, 9, 11, 5];
maxProfit(prices);
// returns 8 (buying for $3 and selling for $11)
```

## Brute Force Solution

Try *every pair of times* treating the earlier time as buy time and the later time as sell time, and see which one is higher.

```
// O(n^2) time
function maxProfit(prices) {
let maxProfit = 0;
for (let i=0; i < prices.length; i++) {
for (let j=0; j < prices.length; j++) {
let earlierTime = Math.min(i, j);
let laterTime = Math.max(i, j);
let earlierPrice = prices[earlierTime];
let laterPrice = prices[laterTime];
let potentialProfit = laterPrice - earlierPrice;
maxProfit = Math.max(maxProfit, potentialProfit);
}
}
return maxProfit;
}
```

One problem: you can never have a negative profit!

## Better Solution

We have to compare every price so *O(n)* is the best we can do. Let’s take a **greedy approach** by keeping a running `maxProfit`

until the end. So for every price check if:

- we can get a better profit by buying at
`minPrice`

and selling at`currentPrice`

- we can have a new
`minPrice`

Initialize `maxProfit`

as the first profit we could get, not `0`

.

```
// O(n) time & O(1) space
function maxProfit(prices) {
let minPrice = prices[0];
let maxProfit = prices[1] - prices[0];
for (let i = 1; i < prices.length; i++) {
let currentPrice = prices[i];
let potentialProfit = currentPrice - minPrice;
maxProfit = Math.max(maxProfit, potentialProfit);
minPrice = Math.min(minPrice, currentPrice);
}
return maxProfit;
}
```

**Want to improve your JavaScript? I have a list of recommended JavaScript books.**