1035. Uncrossed Lines

LeetCode 1035. Uncrossed Lines

Description

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

Note:

1. 1 <= A.length <= 500

2. 1 <= B.length <= 500

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

Tags

Dynamic Programming, Array

Solution

This problem is totally the same as LeetCode 1143. Longest Common Subsequence.

Complexity

• Time complexity: $O(n)$

• Space complexity: $O(n)$

Code

func maxUncrossedLines(nums1 []int, nums2 []int) int {
	dp := make([][]int, len(nums1)+1)
	for i := range dp {
		dp[i] = make([]int, len(nums2)+1)
	}
	for i := 1; i <= len(nums1); i++ {
		for j := 1; j <= len(nums2); j++ {
			if nums1[i-1] == nums2[j-1] {
				dp[i][j] = 1 + dp[i-1][j-1]
			} else {
				dp[i][j] = max(dp[i][j-1], dp[i-1][j])
			}
		}
	}
	return dp[len(nums1)][len(nums2)]
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

Reference

1. 【宫水三叶の相信科学系列】求「最值问题」只需要确保「不漏」即可

2. 不相交的线