Create number-of-ways-to-stay-in-the-same-place-after-some-steps.py

Author: kamyu104

Python/number-of-ways-to-stay-in-the-same-place-after-some-steps.py

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+# Time:  O(n^2), n is the number of steps
+# Space: O(n)
+    
+class Solution(object):
+    def numWays(self, steps, arrLen):
+        """
+        :type steps: int
+        :type arrLen: int
+        :rtype: int
+        """
+        MOD = int(1e9+7)
+        l = min(1+steps//2, arrLen)
+        dp = [0]*(l+2)
+        dp[1] = 1
+        while steps > 0:
+            steps -= 1
+            new_dp = [0]*(l+2)
+            for i in xrange(1, l+1):
+                new_dp[i] = (dp[i] + dp[i-1] + dp[i+1]) % MOD
+            dp = new_dp
+        return dp[1]