Create sum-of-k-mirror-numbers.py

Author: kamyu104

Python/sum-of-k-mirror-numbers.py

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+# Time:  O(10^6), the most times of finding x is 665502 (k = 7, n = 30)
+# Space: O(1)
+
+class Solution(object):
+    def kMirror(self, k, n):
+        """
+        :type k: int
+        :type n: int
+        :rtype: int
+        """
+        def get_mirror(n, base, even):
+            result = n
+            if not even:
+                n //= base
+            while n:
+                result = result*base+n%base
+                n //= base
+            return result
+
+        def reverse(n, base):
+            result = 0
+            while n:
+                result = result*base+n%base
+                n = n//base
+            return result
+
+        result = 0
+        base1, base2 = k, 10  # (10, k) is slower
+        prefix_num, cnt, total = [1]*2, [0]*2, [base1-1]*2
+        even = False
+        for _ in xrange(n):
+            while True:
+                x = get_mirror(prefix_num[even], base1, even)
+                prefix_num[even] += 1
+                cnt[even] += 1
+                if cnt[even] == total[even]:
+                    cnt[even] = 0
+                    total[even] *= base1
+                    even = not even
+                if x == reverse(x, base2):
+                    break
+            result += x
+        return result
+
+
+# Time:  O(10^6), the most times of finding x is 665502 (k = 7, n = 30)
+# Space: O(1)
+class Solution2(object):
+    def kMirror(self, k, n):
+        """
+        :type k: int
+        :type n: int
+        :rtype: int
+        """
+        def num_gen(k):
+            digits = ['0']
+            while True:
+                for i in xrange(len(digits)//2, len(digits)): 
+                    if int(digits[i])+1 < k:
+                        digits[i] = digits[-1-i] = str(int(digits[i])+1)
+                        break
+                    digits[i] = digits[-1-i] = '0'
+                else:
+                    digits.insert(0, '1')
+                    digits[-1] = '1'
+                yield "".join(digits)
+        
+        def mirror_num(gen):
+            while True:
+                x = int(next(gen, k), k)
+                if str(x) == str(x)[::-1]:
+                    break
+            return x
+
+        gen = num_gen(k)
+        return sum(mirror_num(gen) for _ in xrange(n))