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 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.
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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
# Example 1
n = 4, k = 2
5
# Example 2
n = 3, k = 1
3
# Example 3
n = 30, k = 7
796297179
Constraints
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Solve 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, ...
Here's the optimal approach using Math:
Time: O(n) | Space: O(n)
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