Solution.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:
    def minSwap(self, A: List[int], B: List[int]) -> int:
        N = len(A)
        not_swap, swap = [N] * N, [N] * N
        not_swap[0], swap[0] = 0, 1
        for i in range(1, N):
            if A[i - 1] < A[i] and B[i - 1] < B[i]:
                not_swap[i] = not_swap[i - 1]
                swap[i] = swap[i - 1] + 1
            if A[i - 1] < B[i] and B[i - 1] < A[i]:
                not_swap[i] = min(not_swap[i], swap[i - 1])
                swap[i] = min(swap[i], not_swap[i - 1] + 1)
        return min(swap[-1], not_swap[-1])