Create palindrome-partitioning-iii.py

Author: kamyu104

Python/palindrome-partitioning-iii.py

@@ -0,0 +1,29 @@
+# Time:  O(k * n^2)
+# Space: O(n^2)
+
+class Solution(object):
+    def palindromePartition(self, s, k):
+        """
+        :type s: str
+        :type k: int
+        :rtype: int
+        """
+        # dp1[i][j]: minimum number of changes to make s[i, j] palindrome
+        dp1 = [[0]*len(s) for _ in xrange(len(s))]
+        for l in xrange(1, len(s)+1):
+            for i in xrange(len(s)-l+1):
+                j = i+l-1
+                if i == j-1:
+                    dp1[i][j] = 0 if s[i] == s[j] else 1
+                elif i != j:
+                    dp1[i][j] = dp1[i+1][j-1] if s[i] == s[j] else dp1[i+1][j-1]+1
+
+        # dp2[d][i]: minimum number of changes to divide s[0, i] into d palindromes
+        dp2 = [[float("inf")]*len(s) for _ in xrange(2)]
+        dp2[1] = dp1[0][:]
+        for d in xrange(2, k+1):
+            dp2[d%2] = [float("inf")]*len(s)
+            for i in xrange(d-1, len(s)):  
+                for j in xrange(d-2, i):
+                    dp2[d%2][i] = min(dp2[d%2][i], dp2[(d-1)%2][j]+dp1[j+1][i])
+        return dp2[k%2][len(s)-1]