leetcode 188 Best Time to Buy and Sell Stock IV
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 2019-04-09 10:36:27  

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

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

Note:
You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

Example 1:

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Input: [2,4,1], k = 2
Output: 2
Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.

Example 2:

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Input: [3,2,6,5,0,3], k = 2
Output: 7
Explanation: Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6-2 = 4.
             Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
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public class BestTimetoBuyandSellStockIV {
  public int maxProfit(int k, int[] prices) {
    // quick ans if k > len(price)/2
    if (k >= prices.length / 2) {
      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;
    }

    // while k < len(price)/ 2, we need using dp solutions to solve the question.
    // profit[i][j], means the max profit we could get when we have i transactions up to the j-th price;
    int profit[][] = new int[k+1][prices.length];

    for (int i=1; i<=k; i++) {
      int max = -prices[0];
      for (int j=0; j<prices.length; j++) {
        profit[i][j] = Math.max(profit[i][j-1], prices[j] + max);
        max = Math.max(max, profit[i-1][j-1]-prices[j]);
      }
    }
    return profit[k][prices.length-1];
  }
}