Package g3401_3500.s3404_count_special_subsequences

Class Solution

java.lang.Object

g3401_3500.s3404_count_special_subsequences.Solution

public class Solution
extends Object

3404 - Count Special Subsequences.

Medium

You are given an array nums consisting of positive integers.

A special subsequence is defined as a subsequence of length 4, represented by indices (p, q, r, s), where p < q < r < s. This subsequence must satisfy the following conditions:

• nums[p] * nums[r] == nums[q] * nums[s]
• There must be at least one element between each pair of indices. In other words, q - p > 1, r - q > 1 and s - r > 1.

A subsequence is a sequence derived from the array by deleting zero or more elements without changing the order of the remaining elements.

Return the number of different special subsequences in nums.

Example 1:

Input: nums = [1,2,3,4,3,6,1]

Output: 1

Explanation:

There is one special subsequence in nums.

• (p, q, r, s) = (0, 2, 4, 6):
  • This corresponds to elements (1, 3, 3, 1).
  • nums[p] * nums[r] = nums[0] * nums[4] = 1 * 3 = 3
  • nums[q] * nums[s] = nums[2] * nums[6] = 3 * 1 = 3

Example 2:

Input: nums = [3,4,3,4,3,4,3,4]

Output: 3

Explanation:

There are three special subsequences in nums.

• (p, q, r, s) = (0, 2, 4, 6):
  • This corresponds to elements (3, 3, 3, 3).
  • nums[p] * nums[r] = nums[0] * nums[4] = 3 * 3 = 9
  • nums[q] * nums[s] = nums[2] * nums[6] = 3 * 3 = 9
• (p, q, r, s) = (1, 3, 5, 7):
  • This corresponds to elements (4, 4, 4, 4).
  • nums[p] * nums[r] = nums[1] * nums[5] = 4 * 4 = 16
  • nums[q] * nums[s] = nums[3] * nums[7] = 4 * 4 = 16
• (p, q, r, s) = (0, 2, 5, 7):
  • This corresponds to elements (3, 3, 4, 4).
  • nums[p] * nums[r] = nums[0] * nums[5] = 3 * 4 = 12
  • nums[q] * nums[s] = nums[2] * nums[7] = 3 * 4 = 12

Constraints:

• 7 <= nums.length <= 1000
• 1 <= nums[i] <= 1000

Constructor Summary

Constructors

Constructor	Description
Solution()

Method Summary

Modifier and Type	Method	Description
long	numberOfSubsequences(int[] nums)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Solution

public Solution()

Method Details

numberOfSubsequences

public long numberOfSubsequences(int[] nums)