add stock trading DP solution

Author: teckoo

_posts/coding/summary/dynamic_prog/2021-01-01-dp-state-machine.md

@@ -217,4 +217,23 @@ int maxProfit_k_2(int[] prices) {
     }
     return dp_i20;
 }
+```
+
+## 188. k = any integer
+
+```java
+int maxProfit_k_any(int max_k, int[] prices) {
+    int n = prices.length;
+    if (max_k > n / 2) 
+        return maxProfit_k_inf(prices);
+
+    int[][][] dp = new int[n][max_k + 1][2];
+    for (int i = 0; i < n; i++) 
+        for (int k = max_k; k >= 1; k--) {
+            if (i - 1 == -1) { /* 处理 base case */ }
+            dp[i][k][0] = max(dp[i-1][k][0], dp[i-1][k][1] + prices[i]);
+            dp[i][k][1] = max(dp[i-1][k][1], dp[i-1][k-1][0] - prices[i]);     
+        }
+    return dp[n - 1][max_k][0];
+}
 ```