LeetCode - Best Time to Buy and Sell Stock with Transaction Fee

Question Definition

Your are given an array of integers prices, for which the i-th element is the price of a given stock on day i; and a non-negative integer fee representing a transaction fee.

You may complete as many transactions as you like, but you need to pay the transaction fee for each transaction. You may not buy more than 1 share of a stock at a time (ie. you must sell the stock share before you buy again.)

Return the maximum profit you can make.

Example 1:

Input: prices = [1, 3, 2, 8, 4, 9], fee = 2
Output: 8
Explanation: The maximum profit can be achieved by:
* Buying at prices[0] = 1
* Selling at prices[3] = 8
* Buying at prices[4] = 4
Selling at prices[5] = 9
The total profit is ((8 - 1) - 2) + ((9 - 4) - 2) = 8.

Note:

• 0 < prices.length <= 50000.
• 0 < prices[i] < 50000.
• 0 <= fee < 50000.

Analysis

1. Hold stock:
* We do nothing on day i: hold[i - 1];
* We buy stock on day i: notHold[i - 1] - prices[i - 1] - fee;

2. Not hold stock:
* We do nothing on day i: notHold[i - 1];
* We sell stock on day i: hold[i - 1] + prices[i - 1];

Java Solution

public int maxProfit(int[] prices, int fee) {
    int[] hold = new int[prices.length + 1];
    int[] noHold = new int[prices.length + 1];
    hold[0] = Integer.MIN_VALUE;

    for(int i = 1; i <= prices.length; i++){
        hold[i] = Math.max(hold[i - 1], noHold[i - 1] - prices[i - 1] - fee);
        noHold[i] = Math.max(noHold[i - 1], hold[i - 1] + prices[i - 1]);
    }
    return noHold[prices.length];
}