# Problem

https://leetcode.com/problems/minimum-swaps-to-make-sequences-increasing/description/

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: Search/DFS (TLE)

Time complexity: O(2^n)

Space complexity: O(n)

# Solution: DP

Time complexity: O(n)

Space complexity: O(n)

## Python3

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## One Comment

1. koala May 13, 2018

DP的题每次总是差一点。这道题可以想到DFS，想到继续优化应该用DP。但是DP递推式确却想不出来最后正确的，这道题比如得考虑两个元素之间的关系。希望楼主大神可以分享下这个公式如何由一些经验去推导去思考。
自己总结了常见一维，二维，常见字符串，区间DP，DFS+记忆存储，不过碰到新题有些还是一时半会想不出来。
谢谢楼主的视频，讲解非常清晰。