Find the Sum of Subsequence Powers - Practice Coding | SlaveCode
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3098. Find the Sum of Subsequence Powers
Hard
50 Points
Array
Dynamic Programming
Sorting
You are given an integer array nums of length n, and a positive integer k.
The power of a subsequence is defined as the minimum absolute difference between any two elements in the subsequence.
Return the sum of powers of all subsequences of nums which have length equal to k.
Since the answer may be large, return it modulo 109 + 7.
Examples
Example 1
Input: nums = [1,2,3,4], k = 3
Output: 4
Explanation:
There are 4 subsequences in nums which have length 3: [1,2,3] , [1,3,4] , [1,2,4] , and [2,3,4] . The sum of powers is |2 - 3| + |3 - 4| + |2 - 1| + |3 - 4| = 4 .
Example 2
Input: nums = [2,2], k = 2
Output: 0
Explanation:
The only subsequence in nums which has length 2 is [2,2] . The sum of powers is |2 - 2| = 0 .
Example 3
Input: nums = [4,3,-1], k = 2
Output: 10
Explanation:
There are 3 subsequences in nums which have length 2: [4,3] , [4,-1] , and [3,-1] . The sum of powers is |4 - 3| + |4 - (-1)| + |3 - (-1)| = 10 .
Constraints
2 <= n == nums.length <= 50
-108 <= nums[i] <= 108
2 <= k <= n
3098. Find the Sum of Subsequence Powers
Hard
50 Points
Array
Dynamic Programming
Sorting
You are given an integer array nums of length n, and a positive integer k.
The power of a subsequence is defined as the minimum absolute difference between any two elements in the subsequence.
Return the sum of powers of all subsequences of nums which have length equal to k.
Since the answer may be large, return it modulo 109 + 7.
Examples
Example 1
Input: nums = [1,2,3,4], k = 3
Output: 4
Explanation:
There are 4 subsequences in nums which have length 3: [1,2,3] , [1,3,4] , [1,2,4] , and [2,3,4] . The sum of powers is |2 - 3| + |3 - 4| + |2 - 1| + |3 - 4| = 4 .
Example 2
Input: nums = [2,2], k = 2
Output: 0
Explanation:
The only subsequence in nums which has length 2 is [2,2] . The sum of powers is |2 - 2| = 0 .
Example 3
Input: nums = [4,3,-1], k = 2
Output: 10
Explanation:
There are 3 subsequences in nums which have length 2: [4,3] , [4,-1] , and [3,-1] . The sum of powers is |4 - 3| + |4 - (-1)| + |3 - (-1)| = 10 .