# Best Time to Buy and Sell Stock IV

You are given an integer array prices where prices[i] is the price of a given stock on the ith day, and an integer k.

Find the maximum profit you can achieve. You may complete at most k transactions: i.e. you may buy at most k times and sell at most k times.

**Note:** You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).

```
/**
* dp[i, j] represents the max profit up until prices[j] using at most i transactions.
* dp[i, j] = max(dp[i, j-1], prices[j] - prices[jj] + dp[i-1, jj]) { jj in range of [0, j-1] }
* = max(dp[i, j-1], prices[j] + max(dp[i-1, jj] - prices[jj]))
* dp[0, j] = 0; 0 transactions makes 0 profit
* dp[i, 0] = 0; if there is only one price data point you can't make any transaction.
*/
public int maxProfit(int k, int[] prices) {
int n = prices.length;
if (n <= 1)
return 0;
//if k >= n/2, then you can make maximum number of transactions.
if (k >= n/2) {
int maxPro = 0;
for (int i = 1; i < n; i++) {
if (prices[i] > prices[i-1])
maxPro += prices[i] - prices[i-1];
}
return maxPro;
}
int[][] dp = new int[k+1][n];
for (int i = 1; i <= k; i++) {
int localMax = dp[i-1][0] - prices[0];
for (int j = 1; j < n; j++) {
dp[i][j] = Math.max(dp[i][j-1], prices[j] + localMax);
localMax = Math.max(localMax, dp[i-1][j] - prices[j]);
}
}
return dp[k][n-1];
}
```

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