121. Best Time to Buy and Sell Stock

Question

Say you have an array for which the ith 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.

Summary

It will be easy to come up solution of “Brute Force”.

In addition to “Brute Force”, we can have “One Pass” solution. Maintain the “minPrice” and cacuate the “profit” if you sell on the current time.

Solution

class Solution {
public:
    int maxProfit(vector<int>& prices) {
        int profit = 0;
        int minPrice = INT_MAX;
        for (int i=0; i<prices.size(); i++) {
            if (prices[i] < minPrice)
                minPrice = prices[i];
            if (prices[i] - minPrice > profit)
                profit = prices[i] - minPrice;
        }
        return profit;
    }
};