Minimum Swaps To Make Sequences Increasing.py

'''
We have two integer sequences A and B of the same non-zero length.

We are allowed to swap elements A[i] and B[i].  Note that both elements are in the same index position in their respective sequences.

At the end of some number of swaps, A and B are both strictly increasing.  (A sequence is strictly increasing if and only if A[0] < A[1] < A[2] < ... < A[A.length - 1].)

Given A and B, return the minimum number of swaps to make both sequences strictly increasing.  It is guaranteed that the given input always makes it possible.

Example:
Input: A = [1,3,5,4], B = [1,2,3,7]
Output: 1
Explanation: 
Swap A[3] and B[3].  Then the sequences are:
A = [1, 3, 5, 7] and B = [1, 2, 3, 4]
which are both strictly increasing.

Note:

    A, B are arrays with the same length, and that length will be in the range [1, 1000].
    A[i], B[i] are integer values in the range [0, 2000].

'''

class Solution(object):
    def minSwap(self, A, B):
        """
        :type A: List[int]
        :type B: List[int]
        :rtype: int
        """
        assert len(A) == len(B)
        dp = [[float('inf'), float('inf')] for i in xrange(len(A))]
        dp[0][0] = 0
        dp[0][1] = 1
        
        for i in xrange(1, len(A)):
            if A[i] > A[i-1] and B[i] > B[i-1]:
                dp[i][0] = min(dp[i][0], dp[i-1][0])
                dp[i][1] = min(dp[i][1], dp[i-1][1] + 1)
                
            if A[i] > B[i-1] and B[i] > A[i-1]:
                dp[i][0] = min(dp[i][0], dp[i-1][1])
                dp[i][1] = min(dp[i][1], dp[i-1][0] + 1)
                
        return min(dp[-1][0], dp[-1][1])