 # Array - 188. Best Time to Buy and Sell Stock IV

188. Best Time to Buy and Sell Stock IV

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

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

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

Example 1:

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:

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.

java：

``````class Solution {

public int maxProfit(int k, int[] prices) {
int len = prices.length;
if (len == 0) return 0;
if (k >= len/2) return helper(prices);

int[] dp = new int[k+1];
int[] min = new int[k+1];
for (int i = 0; i <min.length; i++) {
min[i] = prices;
}

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

private int helper(int[] p) {
int len = p.length;
int res = 0;

for(int i = 1; i < len; i++) {
if (p[i] > p[i-1]) res += (p[i] - p[i-1]);
}

return res;
}
}
``````

Nothing just happens, it's all part of a plan.