Create additive-number.py

Author: kamyu104

Python/additive-number.py

@@ -0,0 +1,64 @@
+# Time:  O(n^3)
+# Space: O(n)
+#
+# Additive number is a positive integer whose digits can form additive sequence.
+#
+# A valid additive sequence should contain at least three numbers.
+# Except for the first two numbers, each subsequent number in the sequence
+# must be the sum of the preceding two.
+#
+# For example:
+# "112358" is an additive number because the digits can form an additive sequence:
+#   1, 1, 2, 3, 5, 8.
+#
+# 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8
+# "199100199" is also an additive number, the additive sequence is:
+# 1, 99, 100, 199.
+#
+# 1 + 99 = 100, 99 + 100 = 199
+# Note: Numbers in the additive sequence cannot have leading zeros,
+# so sequence 1, 2, 03 or 1, 02, 3 is invalid.
+#
+# Given a string represents an integer, write a function to determine
+# if it's an additive number.
+#
+# Follow up:
+# How would you handle overflow for very large input integers?
+#
+
+class Solution(object):
+    def isAdditiveNumber(self, num):
+        """
+        :type num: str
+        :rtype: bool
+        """
+        def add(a, b):
+            res, carry, val = "", 0, 0
+            for i in xrange(max(len(a), len(b))):
+                val = carry
+                if i < len(a):
+                    val += int(a[-(i + 1)])
+                if i < len(b): 
+                    val += int(b[-(i + 1)])
+                carry, val = val / 10, val % 10
+                res += str(val)
+            if carry:
+                res += str(carry)
+            return res[::-1]
+
+
+        for i in xrange(1, len(num) - 1):
+            for j in xrange(i + 1, len(num)):
+                s1, s2 = num[0:i], num[i:j]
+                if (len(s1) > 1 and s1[0] == '0') or \
+                   (len(s2) > 1 and s2[0] == '0'):
+                    continue
+                
+                expected = add(s1, s2)
+                cur = s1 + s2 + expected
+                while len(cur) < len(num):
+                    s1, s2, expected = s2, expected, add(s2, expected)
+                    cur += expected
+                if cur == num:
+                    return True
+        return False