121 Best Time to Buy and Sell Stock

121. Best Time to Buy and Sell Stock

1. Question

Say you have an array for which thei_thelement 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. Implementation

(1) Greedy

class Solution {
    public int maxProfit(int[] prices) {
        if (prices == null || prices.length == 0) {
            return 0;
        }

        int minPrice = prices[0];
        int maxProfit = 0;

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

3. Time & Space Complexity

时间复杂度O(n), 空间复杂度O(1)