Best Time to Buy and Sell Stokc II

Problem

Say you have an array for which the ith element is the price of a given stock on day i.

Design an algorithm to find the maximum profit. You may complete as many transactions as you like (ie, buy one and sell one share of the stock multiple times). However, you may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

Solution

public class Solution {
    public int maxProfit(int[] prices) {
        if (prices == null || prices.length <= 1) return 0;
        int res = 0;
        for (int i = 1; i < prices.length; i++) {
            if (prices[i] > prices[i - 1]) res += prices[i] - prices[i - 1];
        }
        return res;
    }
}

Analysis

Given prices of stock as [1, 2, 3]
We know the max profit is 2, because we buy at price 1 and sell at price 3
However, we can buy at price 1 and sell at 2 to make 1 profit
Then we buy at 2 and sell at 3 to make another 1 profit
Which at the end will be max profit anyway
This works because the problem allows buy one and sell one share of the stock multiple times

Complexity

• Time: O(n), single pass
• Space: O(1), constant space is used