uncrossed-lines

Uncrossed Lines

LeetCode #: 1035

Difficulty: Medium.

Topics: Array.

Problem

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

Solution Explanation

This problem is similar to the #1143 Longest Common Subsequence problem. The solution is to use dynamic programming by building a two-dimensional table where rows represent values in A and columns represents values in B. The cell values represent the number of connecting lines so far. In the end, the answer will be in the bottom right cell.

Reference: [Java/C++/Python] DP, The Longest Common Subsequence by lee215.

Complexity Analysis

Assume m is the length of array A and n is the length of array B.

Time complexity: O(m*n)

Space complexity: O(m*n)