Algorithm Practice

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123 Best Time to Buy and Sell Stock III

1. Question

ay you have an array for which the*i_thelement is the price of a given stock on day_i*.

Design an algorithm to find the maximum profit. You may complete at most_two_transactions.

Input: [3,3,5,0,0,3,1,4]

Output: 6

Explanation:

Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.

Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 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.

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

Output: 0

Explanation:

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

2. Implementation

class Solution {

public int maxProfit(int[] prices) {

if (prices == null || prices.length == 0) {

return 0;

}

int[][] dp = new int[3][prices.length];

for (int i = 1; i <= 2; i++) {

int holding = -prices[0];

for (int j = 1; j < prices.length; j++) {

dp[i][j] = Math.max(dp[i][j - 1], holding + prices[j]);

holding = Math.max(holding, dp[i - 1][j - 1] - prices[j]);

}

}

return dp[2][prices.length - 1];

}

}

3. Time & Space Complexity

Last modified 2yr ago