DP

public int maxProfit(int k, int[] prices) {
 int len = prices.length;
 if (k >= len / 2) {
 return quickSolve(prices);

 }

 int[][] dp = new int[k + 1][len];

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

 int tmpMax = -prices[0];

 for (int j = 1; j < len; j++) {

 // Sell the stock at j: not sell/sell.

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

 // Buy the stock: not buy/buy.

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

 }

 }

 return dp[k][len - 1];

 }



 private int quickSolve(int[] prices) {

 int len = prices.length, profit = 0;

 for (int i = 1; i < len; i++)

 // as long as there is a price gap, we gain a profit.

 if (prices[i] > prices[i - 1]) {

 profit += prices[i] - prices[i - 1];

 }

 return profit;

 }