1726. Tuple with Same Product
Description
Given an array nums
of distinct positive integers, return the number of tuples (a, b, c, d)
such that a * b = c * d
where a
, b
, c
, and d
are elements of nums
, and a != b != c != d
.
Example 1:
Input: nums = [2,3,4,6] Output: 8 Explanation: There are 8 valid tuples: (2,6,3,4) , (2,6,4,3) , (6,2,3,4) , (6,2,4,3) (3,4,2,6) , (4,3,2,6) , (3,4,6,2) , (4,3,6,2)
Example 2:
Input: nums = [1,2,4,5,10] Output: 16 Explanation: There are 16 valid tuples: (1,10,2,5) , (1,10,5,2) , (10,1,2,5) , (10,1,5,2) (2,5,1,10) , (2,5,10,1) , (5,2,1,10) , (5,2,10,1) (2,10,4,5) , (2,10,5,4) , (10,2,4,5) , (10,2,5,4) (4,5,2,10) , (4,5,10,2) , (5,4,2,10) , (5,4,10,2)
Constraints:
1 <= nums.length <= 1000
1 <= nums[i] <= 104
- All elements in
nums
are distinct.
Solutions
Solution 1: Combination + Hash Table
Assuming there are $n$ pairs of numbers, for any two pairs of numbers $a, b$ and $c, d$ that satisfy the condition $a \times b = c \times d$, there are a total of $\mathrm{C}_n^2 = \frac{n \times (n-1)}{2}$ such combinations.
According to the problem description, each combination that satisfies the above condition can form $8$ tuples that satisfy the problem requirements. Therefore, we can multiply the number of combinations with the same product by $8$ (equivalent to left shifting by $3$ bits) and add them up to get the result.
The time complexity is $O(n^2)$, and the space complexity is $O(n^2)$. Here, $n$ is the length of the array.
1 2 3 4 5 6 7 8 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
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