{leetcode}/problems/number-of-sets-of-k-non-overlapping-line-segments/[LeetCode - 1621. Number of Sets of K Non-Overlapping Line Segments ^]
Given n points on a 1-D plane, where the ith point (from 0 to n-1) is at x = i, find the number of ways we can draw exactly k non-overlapping line segments such that each segment covers two or more points. The endpoints of each segment must have integral coordinates. The k line segments do not have to cover all n points, and they are allowed to share endpoints.
Return the number of ways we can draw _`k` non-overlapping line segments__._ Since this number can be huge, return it modulo 109 + 7.
Example 1: <img alt="" src="https://assets.leetcode.com/uploads/2020/09/07/ex1.png" style="width: 179px; height: 222px;" />
Input: n = 4, k = 2
Output: 5
Explanation: The two line segments are shown in red and blue.
The image above shows the 5 different ways {(0,2),(2,3)}, {(0,1),(1,3)}, {(0,1),(2,3)}, {(1,2),(2,3)}, {(0,1),(1,2)}.
Example 2:
Input: n = 3, k = 1
Output: 3
Explanation: The 3 ways are {(0,1)}, {(0,2)}, {(1,2)}.
Example 3:
Input: n = 30, k = 7 Output: 796297179 Explanation: The total number of possible ways to draw 7 line segments is 3796297200. Taking this number modulo 109 + 7 gives us 796297179.
Constraints:
-
2 ⇐ n ⇐ 1000 -
1 ⇐ k ⇐ n-1