How to Solve Number of Sets of K Non- Overlapping Line Segments Problem
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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 po...
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Understanding the Number of Sets of K Non- Overlapping Line Segments Problem
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Problem Statement
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.
Number of Sets of K Non-Overlapping Line Segments
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Examples
n = 4, k = 25The 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)}.
n = 3, k = 13The 3 ways are {(0,1)}, {(0,2)}, {(1,2)}.
n = 30, k = 7796297179The total number of possible ways to draw 7 line segments is 3796297200. Taking this number modulo 109 + 7 gives us 796297179.
Constraints
2 <= n <= 10001 <= k <= n-1How Interview Coder Helps with Leetcode Problems
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