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// @Title: 买卖股票的最佳时机 IV (Best Time to Buy and Sell Stock IV)
// @Author: 15816537946@163.com
// @Date: 2020-12-28 23:46:46
// @Runtime: 8 ms
// @Memory: 4.7 MB
func maxProfit(k int, prices []int) int {
	n := len(prices)
	if n == 0 {
		return 0
	}

	k = min(k, n/2)
	buy := make([][]int, n)
	sell := make([][]int, n)
	for i := range buy {
		buy[i] = make([]int, k+1)
		sell[i] = make([]int, k+1)
	}
	buy[0][0] = -prices[0]
	for i := 1; i <= k; i++ {
		buy[0][i] = math.MinInt64 / 2
		sell[0][i] = math.MinInt64 / 2
	}

	for i := 1; i < n; i++ {
		buy[i][0] = max(buy[i-1][0], sell[i-1][0]-prices[i])
		for j := 1; j <= k; j++ {
			buy[i][j] = max(buy[i-1][j], sell[i-1][j]-prices[i])
			sell[i][j] = max(sell[i-1][j], buy[i-1][j-1]+prices[i])
		}
	}
	return max(sell[n-1]...)
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a ...int) int {
	res := a[0]
	for _, v := range a[1:] {
		if v > res {
			res = v
		}
	}
	return res
}