sum-of-floored-pairs

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1862. Sum of Floored Pairs (Hard)

Given an integer array nums, return the sum of floor(nums[i] / nums[j]) for all pairs of indices 0 <= i, j < nums.length in the array. Since the answer may be too large, return it modulo 109 + 7.

The floor() function returns the integer part of the division.

 

Example 1:

Input: nums = [2,5,9]
Output: 10
Explanation:
floor(2 / 5) = floor(2 / 9) = floor(5 / 9) = 0
floor(2 / 2) = floor(5 / 5) = floor(9 / 9) = 1
floor(5 / 2) = 2
floor(9 / 2) = 4
floor(9 / 5) = 1
We calculate the floor of the division for every pair of indices in the array then sum them up.

Example 2:

Input: nums = [7,7,7,7,7,7,7]
Output: 49

 

Constraints:

• 1 <= nums.length <= 105
• 1 <= nums[i] <= 105

Related Topics

[Array] [Math] [Binary Search] [Prefix Sum]

Hints

Hint 1

Find the frequency (number of occurrences) of all elements in the array.

Hint 2

For each element, iterate through its multiples and multiply frequencies to find the answer.