Create count-special-integers.py

Author: kamyu104

Python/count-special-integers.py

@@ -0,0 +1,29 @@
+# Time:  O(logn)
+# Space: O(logn)
+
+# combinatorics
+class Solution(object):
+    def countSpecialNumbers(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        def P(m, n):
+            result = 1
+            for _ in xrange(n):
+                result *= m
+                m -= 1
+            return result
+
+        digits = map(int, str(n+1))
+        result = sum(P(9, 1)*P(9, i-1) for i in xrange(1, len(digits)))
+        lookup = set()
+        for i, x in enumerate(digits):
+            for y in xrange(int(i == 0), x):
+                if y in lookup:
+                    continue
+                result += P(9-i, len(digits)-i-1)
+            if x in lookup:
+                break
+            lookup.add(x)
+        return result