1035. Uncrossed Lines

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

1035. Uncrossed Lines
struct Solution;

impl Solution {
    fn max_uncrossed_lines(a: Vec<i32>, b: Vec<i32>) -> i32 {
        let n = a.len();
        let m = b.len();
        let mut dp = vec![vec![0; m + 1]; n + 1];
        for i in 0..n {
            for j in 0..m {
                if a[i] == b[j] {
                    dp[i + 1][j + 1] = dp[i][j] + 1;
                } else {
                    dp[i + 1][j + 1] = dp[i][j + 1].max(dp[i + 1][j]);
                }
            }
        }
        dp[n][m]
    }
}

#[test]
fn test() {
    let a = vec![1, 4, 2];
    let b = vec![1, 2, 4];
    let res = 2;
    assert_eq!(Solution::max_uncrossed_lines(a, b), res);
    let a = vec![2, 5, 1, 2, 5];
    let b = vec![10, 5, 2, 1, 5, 2];
    let res = 3;
    assert_eq!(Solution::max_uncrossed_lines(a, b), res);
    let a = vec![1, 3, 7, 1, 7, 5];
    let b = vec![1, 9, 2, 5, 1];
    let res = 2;
    assert_eq!(Solution::max_uncrossed_lines(a, b), res);
}