188. Best Time to Buy and Sell Stock IV

• Time: $O(nk)$
• Space: $O(k)$

C++JavaPython

class Solution {
 public:
  int maxProfit(int k, vector<int>& prices) {
    if (k >= prices.size() / 2) {
      int sell = 0;
      int hold = INT_MIN;

      for (const int price : prices) {
        sell = max(sell, hold + price);
        hold = max(hold, sell - price);
      }

      return sell;
    }

    vector<int> sell(k + 1);
    vector<int> hold(k + 1, INT_MIN);

    for (const int price : prices)
      for (int i = k; i > 0; --i) {
        sell[i] = max(sell[i], hold[i] + price);
        hold[i] = max(hold[i], sell[i - 1] - price);
      }

    return sell[k];
  }
};

class Solution {
  public int maxProfit(int k, int[] prices) {
    if (k >= prices.length / 2) {
      int sell = 0;
      int hold = Integer.MIN_VALUE;

      for (final int price : prices) {
        sell = Math.max(sell, hold + price);
        hold = Math.max(hold, sell - price);
      }

      return sell;
    }

    int[] sell = new int[k + 1];
    int[] hold = new int[k + 1];
    Arrays.fill(hold, Integer.MIN_VALUE);

    for (final int price : prices)
      for (int i = k; i > 0; --i) {
        sell[i] = Math.max(sell[i], hold[i] + price);
        hold[i] = Math.max(hold[i], sell[i - 1] - price);
      }

    return sell[k];
  }
}

class Solution:
  def maxProfit(self, k: int, prices: list[int]) -> int:
    if k >= len(prices) // 2:
      sell = 0
      hold = -math.inf

      for price in prices:
        sell = max(sell, hold + price)
        hold = max(hold, sell - price)

      return sell

    sell = [0] * (k + 1)
    hold = [-math.inf] * (k + 1)

    for price in prices:
      for i in range(k, 0, -1):
        sell[i] = max(sell[i], hold[i] + price)
        hold[i] = max(hold[i], sell[i - 1] - price)

    return sell[k]