Create super-palindromes.py

Python/super-palindromes.py

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+# Time:  O(n^0.25 * logn)
+# Space: O(logn)
+
+# Let's say a positive integer is a superpalindrome
+# if it is a palindrome, and it is also the square of a palindrome.
+#
+# Now, given two positive integers L and R (represented as strings),
+# return the number of superpalindromes in the inclusive range [L, R].
+#
+# Example 1:
+#
+# Input: L = "4", R = "1000"
+# Output: 4
+# Explanation: 4, 9, 121, and 484 are superpalindromes.
+# Note that 676 is not a superpalindrome: 26 * 26 = 676,
+# but 26 is not a palindrome.
+#
+# Note:
+# - 1 <= len(L) <= 18
+# - 1 <= len(R) <= 18
+# - L and R are strings representing integers in the range [1, 10^18).
+# - int(L) <= int(R)
+
+class Solution(object):
+    def superpalindromesInRange(self, L, R):
+        """
+        :type L: str
+        :type R: str
+        :rtype: int
+        """
+        def is_palindrome(k):
+            return str(k) == str(k)[::-1]
+
+        K = int((10**((len(R)+1)*0.25)))
+        l, r = int(L), int(R)
+
+        result = 0
+
+        # count odd length
+        for k in xrange(K):
+            s = str(k)
+            t = s + s[-2::-1]
+            v = int(t)**2
+            if v > r:
+                break
+            if v >= l and is_palindrome(v):
+                result += 1
+
+        # count even length
+        for k in xrange(K):
+            s = str(k)
+            t = s + s[::-1]
+            v = int(t)**2
+            if v > r:
+                break
+            if v >= l and is_palindrome(v):
+                result += 1
+
+        return result