LeetCode-in-Java
3098. Find the Sum of Subsequence Powers
Hard
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.
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] <= 1082 <= k <= n
Solution
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
public class Solution {
private static final int MOD = 1_000_000_007;
private int len;
private int dfs(int lastIdx, int k, int minDiff, Map<Long, Integer> dp, int[] nums) {
if (k == 0) {
return minDiff;
}
long key = (((long) minDiff) << 12) + ((long) lastIdx << 6) + k;
if (dp.containsKey(key)) {
return dp.get(key);
}
int res = 0;
for (int i = lastIdx + 1; i <= len - k; i++) {
res = (res + dfs(i, k - 1, Math.min(minDiff, nums[i] - nums[lastIdx]), dp, nums)) % MOD;
}
dp.put(key, res);
return res;
}
public int sumOfPowers(int[] nums, int k) {
len = nums.length;
Arrays.sort(nums);
Map<Long, Integer> dp = new HashMap<>();
int res = 0;
for (int i = 0; i <= len - k; i++) {
res = (res + dfs(i, k - 1, nums[len - 1] - nums[0], dp, nums)) % MOD;
}
return res;
}
}