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## Problem

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.

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

Example 1:

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


Example 2:

Input: k = 2, prices = [3,2,6,5,0,3]
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.


## Code

class Solution {
public int maxProfit(int k, int[] prices) {
int len = prices.length;

if(k >= len / 2) return helper(prices);

int[][] dp = new int[k + 1][prices.length];

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

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

}
return dp[k][prices.length - 1];
}

private int helper(int[] prices){
int res = 0;
for(int i = 1; i < prices.length; i++){
if(prices[i] > prices[i - 1]){
res += prices[i] - prices[i - 1];
}
}

return res;
}
}