The general idea is DP, while I had to add a "quickSolve" function to tackle some corner cases to avoid TLE.

DP: t(i,j) is the max profit for up to i transactions by time j (0<=i<=K, 0<=j<=T).

```
public int maxProfit(int k, int[] prices) {
int len = prices.length;
if (k >= len / 2) return quickSolve(prices);
int[][] t = new int[k + 1][len];
for (int i = 1; i <= k; i++) {
int tmpMax = -prices[0];
for (int j = 1; j < len; j++) {
t[i][j] = Math.max(t[i][j - 1], prices[j] + tmpMax);
tmpMax = Math.max(tmpMax, t[i - 1][j - 1] - prices[j]);
}
}
return t[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;
}
```