121. Best Time to Buy and Sell Stock.md

121. Best Time to Buy and Sell Stock

1. Description

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.

2. Solutions

Solution 1: Language: C Brute Force

A double-loop has been used to update the maximum profit.

• Wednesday, 14 October, 2020
• Time Complexity: $O(n^{2})$
• Space Complexity: $O(1)$
• Runtime: 804 ms, faster than 19.13% of C online submissions for Best Time to Buy and Sell Stock.
• Memory Usage: 7 MB, less than 52.13% of C online submissions for Best Time to Buy and Sell Stock.

// Just like "1. Two Sum", we use two loops to find the maximum difference.
int maxProfit(int *prices, int pricesSize) {
    int maxProfit = 0;
    for (int i = 0; i < pricesSize; i++) {
        for (int j = i + 1; j < pricesSize; j++) {
            int currentProfit = prices[j] - prices[i];
            if (currentProfit > maxProfit) {
                maxProfit = currentProfit;
            }
        }
    }
    return maxProfit;
}