Package g1601_1700.s1621_number_of_sets_of_k_non_overlapping_line_segments

Class Solution

  • public class Solution
extends Object
    1621 - Number of Sets of K Non-Overlapping Line Segments.

    Medium

    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:

    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

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • numberOfSets

        public int numberOfSets​(int n,
                        int k)