Create number-of-ways-to-rearrange-sticks-with-k-sticks-visible.py

Author: kamyu104

Python/number-of-ways-to-rearrange-sticks-with-k-sticks-visible.py

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+# Time:  O(n * k)
+# Space: O(k)
+
+class Solution(object):
+    def rearrangeSticks(self, n, k):
+        """
+        :type n: int
+        :type k: int
+        :rtype: int
+        """
+        MOD = 10**9+7
+        dp = [[0 for _ in xrange(k+1)] for _ in xrange(2)]
+        dp[1][1] = 1
+        for i in xrange(2, n+1):
+            for j in xrange(1, min(i, k)+1):
+                # choose the tallest as the last one which would be visible:    dp[i-1][j-1]
+                # choose the non-tallest as the last one which would be hidden: (i-1)*dp[i-1][j]
+                dp[i%2][j] = (dp[(i-1)%2][j-1]+(i-1)*dp[(i-1)%2][j]) % MOD 
+        return dp[n%2][k]