Merge pull request #242 from jeantimex/rotated-digits

Rotated Digits

Author: jeantimex

README.md

@@ -109,6 +109,7 @@ A collection of JavaScript problems and solutions for studying algorithms.
 - [Sort Characters By Frequency](src/string/sort-characters-by-frequency.js)
 - [Binary Watch](src/string/binary-watch.js)
 - [Magical String](src/string/magic-string.js)
+- [Rotated Digits](src/string/rotated-digits.js)
 
 ### Sorting
 

src/string/rotated-digits.js

@@ -0,0 +1,60 @@
+/**
+ * Rotated Digits
+ *
+ * X is a good number if after rotating each digit individually by 180 degrees,
+ * we get a valid number that is different from X.  Each digit must be rotated - we cannot choose to leave it alone.
+ *
+ * A number is valid if each digit remains a digit after rotation. 0, 1, and 8 rotate to themselves; 2 and 5
+ * rotate to  * each other; 6 and 9 rotate to each other, and the rest of the numbers do not rotate to any
+ * other number and become  * invalid.
+ *
+ * Now given a positive number N, how many numbers X from 1 to N are good?
+ *
+ * Example:
+ * Input: 10
+ * Output: 4
+ *
+ * Explanation:
+ * There are four good numbers in the range [1, 10] : 2, 5, 6, 9.
+ *
+ * Note that 1 and 10 are not good numbers, since they remain unchanged after rotating.
+ *
+ * Note:
+ *
+ * N  will be in range [1, 10000].
+ */
+
+/**
+ * @param {number} N
+ * @return {number}
+ */
+const rotatedDigits = N => {
+  // Count how many n in [1, N] are good.
+  let ans = 0;
+
+  for (let n = 1; n <= N; ++n) {
+    if (isGood(n, false)) ans++;
+  }
+
+  return ans;
+};
+
+// Return true if n is good.
+// The flag is true iff we have an occurrence of 2, 5, 6, 9.
+const isGood = (n, flag) => {
+  if (n == 0) return flag;
+
+  const d = n % 10;
+
+  if (d == 3 || d == 4 || d == 7) {
+    return false;
+  }
+
+  if (d == 0 || d == 1 || d == 8) {
+    return isGood(Math.floor(n / 10), flag);
+  }
+
+  return isGood(Math.floor(n / 10), true);
+};
+
+export { rotatedDigits };