Is 3Sum With Multiplicity easy or hard?

The problem is generally classified as Medium difficulty. The core logic resembles the classic 3Sum pattern, but correctly counting duplicates and computing multiplicities adds an extra layer of reasoning compared with simpler triplet problems.

3Sum With Multiplicity Python/Java solution

Python and Java implementations commonly sort the array and apply a two‑pointer scan for each fixed index. The logic counts duplicates on both sides when a valid sum is found. Another implementation uses a HashMap or dictionary to store frequencies and compute combinations for repeated values.

How to solve 3Sum With Multiplicity in O(n)?

A strict O(n) solution is generally not achievable because the algorithm must consider pairs of numbers to determine the third value. The best practical complexity is O(n^2), either with sorting plus two pointers or by iterating pairs with a hashmap frequency count.

What is the best approach for 3Sum With Multiplicity?

The most common interview solution sorts the array and applies the two pointers technique. Fix one number, then move two pointers across the remaining subarray to find pairs that complete the target sum. Duplicate values are counted using combinational logic, giving O(n^2) time and O(1) extra space.

Is 3Sum With Multiplicity asked at Google/Amazon/Meta?

3Sum‑style problems are common in interviews at companies like Amazon, Google, and Meta because they test array manipulation, duplicate handling, and two‑pointer reasoning. Variants such as 3Sum, 3Sum Closest, and 3Sum With Multiplicity appear frequently in technical interview practice sets.

What data structure is used in 3Sum With Multiplicity?

Typical implementations rely on arrays combined with either the two pointers technique after sorting or a hashmap for frequency counting. The hashmap approach tracks how many times each value appears, enabling efficient combinational counting of valid triplets.

What is the time complexity of 3Sum With Multiplicity?

Most efficient solutions run in O(n^2) time. The array is sorted once in O(n log n), then each element is used as a starting point while a two‑pointer scan processes the remaining elements. Space complexity can be O(1) with the two‑pointer method or O(n) when using a hashmap frequency table.

Description Solution Video 10:56

923. 3Sum With Multiplicity

Medium46.2% acceptance4 companies

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 10⁹ + 7.

Example 1:

Input: arr = [1,1,2,2,3,3,4,4,5,5], target = 8
Output: 20
Explanation: 
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
Explanation: 
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
Explanation: (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

Asked at 4 companies

Quora

Google Amazon Meta

Topics

10:56

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1class Solution:
2    def threeSumMulti(self, arr: List[int], target: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[1,1,2,2,3,3,4,4,5,5]
8

Input

[1,1,2,2,2,2]
5

Input

[2,1,3]
6

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