3Sum With Multiplicity — LeetCode 923 Python Solution

The problem

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

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]):

Python solution

class Solution:
    def threeSumMulti(self, arr: List[int], target: int) -> int:
        mod = 10**9 + 7
        cnt = Counter(arr)
        ans = 0
        for j, b in enumerate(arr):
            cnt[b] -= 1
            for a in arr[:j]:
                c = target - a - b
                ans = (ans + cnt[c]) % mod
        return ans

Complexity

Pattern: Two Pointers

Use the order already in the input to discard half the search space at every step. LeetCode 923. 3Sum With Multiplicity is filed here because LeetCode tags it Two Pointers, which is the vocabulary this hub collects.

The two pointers guide has the Python template for the pattern and the 201 LeetCode problems that use it.

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