Sum of Floored Pairs

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Problem Statement

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 10 ^9 + 7 .

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

Examples

Example 1

Input: nums = [2,5,9]
Output: 10
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 <= 10 ^5

1 <= nums[i] <= 10 ^5

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicMath