Array | Learn for Master

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 (ie, buy one and sell one share of the stock), design an algorithm to find the maximum profit.

Example 1:

Input: [7, 1, 5, 3, 6, 4]
Output: 5
max. difference = 6-1 = 5 (not 7-1 = 6, as selling price needs to be larger than buying price)

Input: [7, 1, 5, 3, 6, 4]

Output: 5

max. difference = 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
In this case, no transaction is done, i.e. max profit = 0.

Input: [7, 6, 4, 3, 1]

Output: 0

In this case, no transaction is done, i.e. max profit = 0.

Analysis:

We scan the table, and record the minimum price in the range [0, i - 1], so the potential max profit is prices[i] - min(prices[0, i-1])
The following is the implementation in Java:

public class BestTimetoBuyandSellStock {
    public int maxProfit(int[] prices) {
        if (prices.length == 0) {
            return 0;
        }
        int maxProfit = 0;
        int minPrice = prices[0];
        for (int i = 1; i < prices.length; i++) {
            maxProfit = Math.max(maxProfit, prices[i] - minPrice);
            minPrice = Math.min(minPrice, prices[i]);
        }
        return maxProfit;
    }
}
}