状态分类：

f[i,j,0]考虑前i只股票，进行了j笔交易，目前未持有股票 所能获得最大利润

f[i,j,1]考虑前i只股票，进行了j笔交易，目前持有股票 所能获得最大利润

状态转移：

f[i][j][0] = Math.max(f[i-1][j][0],f[i-1][j][1]+prices[i]);

f[i][j][1] = Math.max(f[i-1][j][1],f[i-1][j-1][0]-prices[i]);

 

class Solution {
    static int INF = 0x3f3f3f3f;
    public int maxProfit(int k, int[] prices) {
        int n = prices.length;
        int f[][][] = new int[n+1][k+1][2];
        for(int i = 0;i <= n;i++){
            for(int j = 0;j <= k;j++){
                Arrays.fill(f[i][j],-INF);
            }
            
        }
        for(int i = 0;i <= n;i++)f[i][0][0] = 0;

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

还有一位大佬的看不懂的极妙解法--滚动的dp？

// java
class Solution {
    public int maxProfit(int k, int[] prices) {
        int[] buy = new int[k], sell = new int[k];
        Arrays.fill(buy, -prices[0]);
        for (int i = 1; i < prices.length; i++) {
            for (int j = 0, pre = 0; j < k; j++) {
                buy[j] = (pre = Math.max(buy[j], pre - prices[i]));
                sell[j] = (pre = Math.max(sell[j], pre + prices[i]));
            }
        }
        return Math.max(sell[k - 1], 0);
    }
}