Class Solution
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
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Constructor Summary
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Method Summary
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Constructor Details
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Solution
public Solution()
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Method Details
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numberOfSets
public int numberOfSets(int n, int k)
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