Aug20: ways to reach k-th stair [H][DP]

Another DP problem w/ states

daily/Aug20.cc

@@ -0,0 +1,33 @@
+#include <unordered_map>
+using namespace std;
+
+class Solution {
+ public:
+  /**
+   * @brief LC3154: Find number of ways to Reach k-th stair [H][DP][State][Memo]
+   * Time: O()
+   *
+   * @param k
+   * @return int
+   */
+  int waysToReachStair(int k) {
+    unordered_map<long long, int> memo;
+    auto dfs = [&](auto&& dfs, int i, int j, bool pre_down) -> int {
+      if (i > k + 1) {  // can't to k
+        return 0;
+      }
+      // compress (i, j, pre_down) to long long
+      long long mask = (long long)i << 32 | j << 1 | pre_down;
+      if (memo.find(mask) != memo.end()) {
+        return memo[mask];  // computed before
+      }
+      int res = i == k;
+      res += dfs(dfs, i + (1 << j), j + 1, false);  // op2
+      if (i && !pre_down) {
+        res += dfs(dfs, i - 1, j, true);  // op1
+      }
+      return memo[mask] = res;  // memo
+    };
+    return dfs(dfs, 1, 0, false);
+  }
+};