Minimum Swaps To Make Sequences Increasing
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 < A < A < ... < 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.
Input: A = [1,3,5,4], B = [1,2,3,7] Output: 1 Explanation: Swap A and B. Then the sequences are: A = [1, 3, 5, 7] and B = [1, 2, 3, 4] which are both strictly increasing.
- 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].
Credits To: leetcode.com
Leave me comments, if you have better ways to solve.
## Blog link: https://code.dennyzhang.com/minimum-swaps-to-make-sequences-increasing ## Basic Ideas: dynamic programming ## ## If examining two adjacent columns, there are only 2 combinations! ## ## dp[i]: swap or don't swap current item ## ## Complexity: Time O(n), Space O(n) class Solution: def minSwap(self, A, B): """ :type A: List[int] :type B: List[int] :rtype: int """ import sys length = len(A) dp = [[sys.maxsize, sys.maxsize] for i in range(length)] dp = [0, 1] for i in range(1, length): # case1: don't swap if A[i]>A[i-1] and B[i]>B[i-1]: dp[i] = min(dp[i], dp[i-1]) dp[i] = min(dp[i], dp[i-1] + 1) # case2: swap if A[i]>B[i-1] and B[i]>A[i-1]: dp[i] = min(dp[i], dp[i-1]) dp[i] = min(dp[i], dp[i-1] + 1) return min(dp[-1], dp[-1])