solved: 779

Author: ryoppippi

code/779.k-th-symbol-in-grammar.ts

@@ -0,0 +1,31 @@
+// @leet start
+
+/**
+ * compare to row4 & row5
+ *
+ * row4 : 01101001
+ * row5 : 011010011001011
+ *
+ * so we can see that row5 is row4 + row4's reverse
+ *
+ * row5 : row4 + reverse(row4)
+ * -> recursion!!!!
+ *
+ * if k <= mid: the nth in row-n is the same as the kth in row-(n-1)
+ * if k > mid: the nth in row-n is the opposite of the kth in row-(n-1)
+ */
+function kthGrammar(n: number, k: number): number {
+  if (n === 1) {
+    return 0;
+  }
+
+  const mid = 2 ** (n - 1) / 2;
+
+  if (k <= mid) {
+    return kthGrammar(n - 1, k);
+  } else {
+    return 1 - kthGrammar(n - 1, k - mid);
+  }
+}
+// @leet end
+