Create number-of-subsequences-with-odd-sum.py

Author: kamyu104

Python/number-of-subsequences-with-odd-sum.py

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+# Time:  O(n)
+# Space: O(1)
+
+# combinatorics, fast exponentiation
+class Solution(object):
+    def subsequenceCount(self, nums):
+        """
+        :type nums: List[int]
+        :rtype: int
+        """
+        MOD = 10**9+7
+        # 2^(odd-1)*2^even = 2^(len(nums)-1)
+        return pow(2, len(nums)-1, MOD) if any(x%2 for x in nums) else 0
+
+
+# Time:  O(n)
+# Space: O(1)
+# dp
+class Solution2(object):
+    def subsequenceCount(self, nums):
+        """
+        :type nums: List[int]
+        :rtype: int
+        """
+        MOD = 10**9+7
+        dp = [0]*2
+        for x in nums:
+            dp = [(dp[i]+dp[i^(x%2)]+int(x%2 == i))%MOD for i in xrange(2)]
+        return dp[1]