g1601_1700.s1621_number_of_sets_of_k_non_overlapping_line_segments

Class Solution

java.lang.Object

g1601_1700.s1621_number_of_sets_of_k_non_overlapping_line_segments.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 Summary

Constructors

Constructor and Description
Solution()

Method Summary

Modifier and Type	Method and Description
int	numberOfSets(int n, int k)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Solution

public Solution()

Method Detail

numberOfSets

public int numberOfSets(int n,
                        int k)