3Sum Closest

From LeetCode

problem description / no solution provided

Solution in Python3

from bisect import bisect, bisect_left

class Solution:
    def threeSumClosest(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
        """
        nums = sorted(nums)

        # Let top[i] be the sum of largest i numbers.
        top = [
            0,
            nums[-1],
            nums[-1] + nums[-2]
        ]

        min_diff = float('inf')
        three_sum = 0

        # Find range of the least number in curr_n (0, 1, 2 or 3)
        # numbers that sum up to curr_target, then find range of 
        # 2nd least number and so on by recursion. 
        def closest(curr_target, curr_n, lo=0):
            if curr_n == 0:
                nonlocal min_diff, three_sum
                if abs(curr_target) < min_diff:
                    min_diff = abs(curr_target)
                    three_sum = target - curr_target
                return
            
            next_n = curr_n - 1
            max_i = len(nums) - curr_n
            max_i = bisect(
                nums, curr_target // curr_n,
                lo, max_i)
            min_i = bisect_left(
                nums, curr_target - top[next_n],
                lo, max_i) - 1
            min_i = max(min_i, lo)

            for i in range(min_i, max_i + 1): 
                if min_diff == 0:
                    return
                if i == min_i or nums[i] != nums[i - 1]:
                    next_target = curr_target - nums[i]
                    closest(next_target, next_n, i + 1)

        closest(target, 3)
        return three_sum

I am lucky to get

Runtime: 52 ms, faster than 98.13% of Python3 online submissions for 3Sum Closest.

Time Complexity

\(O(n^2 log{n})\), where \(n\) is the number of numbers.

• Binary search function bisect takes \(\log{n}\).
• The range of last number is \(O(1)\) since curr_n is 1 and top[next_n] is 0. So given first 2 numbers, find the closest triplet takes \(\log{n}\).

Variants

Two pointers

Similar to 3Sum’s two pointers approach. sample