title

problem link

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].

solution

class Solution:
    def minSwap(self, A: List[int], B: List[int]) -> int:
        # enum: k=0, not swap, k=1, swap
        N = len(A)
        dp = [[N] * 2 for _ in range(N + 1)]
        dp[0] = [0, 1]
        for i in range(1, N):
            a, a1, b, b1 = A[i - 1], A[i], B[i - 1], B[i]
            if a1 > a and b1 > b:
                dp[i][0] = min(dp[i][0], dp[i - 1][0])
                dp[i][1] = min(dp[i][1], dp[i - 1][1] + 1)
            if a1 > b and b1 > a:
                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[N-1])