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).

On each day, you may decide to buy and/or sell the stock. You can only hold at most one share of the stock at any time. However, you can buy it then immediately sell it on the same day.

Find and return the maximum profit you can achieve.

Examples

Example 1:

Input : [1 2 3]
Return : 2

Example 2:

Input: [7,1,5,3,6,4]
Output: 7
Explanation: Buy on day 2 (price = 1) and sell on day 3 (price = 5), profit = 5-1 = 4.
             Then buy on day 4 (price = 3) and sell on day 5 (price = 6), profit = 6-3 = 3.

Example 3:

Input: [1,2,3,4,5]
Output: 4
Explanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.
             Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are
             engaging multiple transactions at the same time. You must sell before buying again.

Example 4

Input: [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.

Solution

Getting max profit This problem can be viewed as finding all ascending sequences. For example, given {5, 1, 2, 3, 4}, buy at 1 & sell at 4 is the same as buy at 1 & sell at 2, buy at 2 & sell at 3,  buy at 3 & sell at 4.

We can scan the array once, and find all pairs of elements that are in ascending order.

Method 1 - Just See if We Can Make Profit

We can loop on the array see if we can make any profit on the adjacent values.

Code

Java
public int maxProfit(int[] prices) {
	int profit = 0;

	for (int i = 1; i<prices.length; i++) {
		if (prices[i] > prices[i - 1]) {
			profit += prices[i] - prices[i - 1];
		}
	}

	return profit;
}