[leetcode] problem 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

No.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.

No.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.

Code

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public int (int k, int[] prices) {
int n = prices.length;

if (n == 0)
return 0;

if (k >= n)
return maxProfit(prices);

int[] T = new int[n];
int[] prev = new int[n];

for (int j = 1; j <= k; j++) {
int maxDiff = -prices[0];

for (int i = 1; i < n; i++) {
T[i] = Math.max(T[i - 1], prices[i] + maxDiff);
maxDiff = Math.max(maxDiff, prev[i] - prices[i]);
prev[i] = T[i];
}
}

return T[n - 1];
}

private int (int[] prices) {
int result = 0;

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

return result;
}