Create numbers-with-repeated-digits.py

Author: kamyu104

Python/numbers-with-repeated-digits.py

@@ -0,0 +1,41 @@
+# Time:  O(logn)
+# Space: O(logn)
+
+class Solution(object):
+    def numDupDigitsAtMostN(self, N):
+        """
+        :type N: int
+        :rtype: int
+        """
+        def P(m, n):
+            result = 1
+            while n > 0:
+                result *= m-n+1
+                n -= 1
+            return result
+
+        digits = map(int, str(N+1))
+        result = 0
+
+        # Given 321
+        #
+        # 1. count numbers without repeated digits:
+        # - X
+        # - XX
+        for i in xrange(1, len(digits)):
+            result += P(9, 1)*P(9, i-1)
+        
+        # 2. count numbers without repeated digits:
+        # - 1XX ~ 3XX
+        # - 30X ~ 32X
+        # - 320 ~ 321
+        prefix_set = set()
+        for i, x in enumerate(digits):
+            for y in xrange(1 if i == 0 else 0, x):
+                if y in prefix_set:
+                    continue
+                result += P(9-i, len(digits)-i-1)
+            if x in prefix_set:
+                break
+            prefix_set.add(x)
+        return N-result