【leetcode】1035. Uncrossed Lines

题目以下：

We write the integers of A and B (in the order they are given) on two separate horizontal lines.

Now, we may draw connecting lines: a straight line connecting two numbers A[i] and B[j] such that:

• A[i] == B[j];
• The line we draw does not intersect any other connecting (non-horizontal) line.

Note that a connecting lines cannot intersect even at the endpoints: each number can only belong to one connecting line.

Return the maximum number of connecting lines we can draw in this way.

 

Example 1:

Input: A = [1,4,2], B = [1,2,4] Output: 2 Explanation: We can draw 2 uncrossed lines as in the diagram. We cannot draw 3 uncrossed lines, because the line from A[1]=4 to B[2]=4 will intersect the line from A[2]=2 to B[1]=2. 

Example 2:

Input: A = [2,5,1,2,5], B = [10,5,2,1,5,2] Output: 3 

Example 3:

Input: A = [1,3,7,1,7,5], B = [1,9,2,5,1] Output: 2

 

Note:

1. 1 <= A.length <= 500
2. 1 <= B.length <= 500
3. 1 <= A[i], B[i] <= 2000

解题思路：本题能够采用动态规划的方法。记dp[i][j]为A[i]与B[j]连线后能够组成的最多连线的数量，固然这里A[i]与B[j]连线是虚拟的连线，所以存在A[i] != B[j]的状况。首先来看A[i] == B[j]，这说明A[i]与B[i]能够连线，显然有dp[i][j] = dp[i-1][j-1]+1；若是是A[i] != B[j]，那么分为三种状况dp[i][j] = max(dp[i-1][j-1],dp[i][j-1],dp[i-1][j])，这是由于A[i]不与B[j]连线，可是A[i]可能能够与B[j]以前全部点的连线，同理B[j]也是同样的。

代码以下：

class Solution(object): def maxUncrossedLines(self, A, B): """ :type A: List[int] :type B: List[int] :rtype: int """ dp = [] for i in range(len(A)): dp.append([0] * len(B)) for i in range(len(A)): for j in range(len(B)): if A[i] == B[j]: dp[i][j] = max(dp[i][j],1) if i - 1 >= 0 and j - 1 >= 0 : dp[i][j] = max(dp[i][j],dp[i-1][j-1]+1) else: if i - 1 >= 0 and j - 1 >= 0: dp[i][j] = max(dp[i][j],dp[i-1][j-1]) if j - 1 >= 0: dp[i][j] = max(dp[i][j],dp[i][j-1]) if i - 1 >= 0: dp[i][j] = max(dp[i][j],dp[i-1][j]) return dp[-1][-1]