动态规划-状态机（188. 买卖股票的最佳时机 IV）

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);}
}