3Sum With Multiplicity

arrayhash tabletwo pointers

Problem Statement

Given an integer array arr , and an integer target , return the number of tuples i, j, k such that i < j < k and arr[i] + arr[j] + arr[k] == target .

As the answer can be very large, return it modulo 10 ^9 + 7 .

Examples

Example 1

Input: arr = [1,1,2,2,3,3,4,4,5,5], target = 8
Output: 20
Enumerating by the values (arr[i], arr[j], arr[k]):
(1, 2, 5) occurs 8 times;
(1, 3, 4) occurs 8 times;
(2, 2, 4) occurs 2 times;
(2, 3, 3) occurs 2 times.

Example 2

Input: arr = [1,1,2,2,2,2], target = 5
Output: 12
arr[i] = 1, arr[j] = arr[k] = 2 occurs 12 times:
We choose one 1 from [1,1] in 2 ways,
and two 2s from [2,2,2,2] in 6 ways.

Example 3

Input: arr = [2,1,3], target = 6
Output: 1
(1, 2, 3) occured one time in the array so we return 1.

Constraints

3 <= arr.length <= 3000

0 <= arr[i] <= 100

0 <= target <= 300

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicHash Table