Paint Fence

Author: saurabhchris1

Paint_Fence.py

@@ -0,0 +1,39 @@
+# There is a fence with n posts, each post can be painted with one of the k colors.
+#
+# You have to paint all the posts such that no more than two adjacent fence posts have the same color.
+#
+# Return the total number of ways you can paint the fence.
+#
+# Note:
+# n and k are non-negative integers.
+#
+# Example:
+#
+# Input: n = 3, k = 2
+# Output: 6
+# Explanation: Take c1 as color 1, c2 as color 2. All possible ways are:
+#
+#             post1  post2  post3
+#  -----      -----  -----  -----
+#    1         c1     c1     c2
+#    2         c1     c2     c1
+#    3         c1     c2     c2
+#    4         c2     c1     c1
+#    5         c2     c1     c2
+#    6         c2     c2     c1
+
+
+class Solution:
+    def numWays(self, n, k):
+
+        if n == 0:
+            return 0
+        if n == 1:
+            return k
+
+        same, diff = k, k * (k - 1)
+
+        for i in range(3, n + 1):
+            same, diff = diff, (same + diff) * (k - 1)
+
+        return same + diff