3Sum Closest
Problem Description: Given an array nums of n integers and an integer target, find three integers in nums such that the sum is closest to target. Return the sum of the three integers.
Example:
python
# Example usage of the function
nums = [-1, 2, 1, -4]
target = 1
closest_sum = threeSumClosest(nums, target)
# The closest sum to the target 1 is (-1 + 2 + 1) = 2
1. Clarify the problem: Before starting, let's ask some clarifying questions to ensure we fully understand the problem requirements:
- Can the given array contain duplicate elements?
- Can the given array be empty?
- Can the value of target be negative or zero?
2. Analyze the problem: Let's break down the problem to better understand its components:
- Input: An array of integers
nums
with lengthn
and an integertarget
. - Output: The sum of three integers from
nums
that is closest to thetarget
. - Constraints: The length of
nums
is at least 3, and the range of the elements is within the 32-bit signed integer range.
3. Design an algorithm: To find the three integers whose sum is closest to the target, we can follow these steps:
- Sort the array
nums
in non-decreasing order. - Initialize a variable
closest_sum
to store the closest sum found so far. Set it to a large value initially. - Iterate through the array
nums
from left to right, considering each element as the potential first element of the triplet.- For the current element, use two pointers,
left
andright
, initialized to the next element and the last element of the remaining array, respectively. - Calculate the current sum of the three elements:
current_sum = nums[i] + nums[left] + nums[right]
. - Update
closest_sum
if the absolute difference betweencurrent_sum
andtarget
is smaller than the absolute difference betweenclosest_sum
andtarget
. - If
current_sum
is greater thantarget
, decrementright
to try a smaller value. Otherwise, incrementleft
to try a larger value.
- For the current element, use two pointers,
- Repeat the above steps for all elements of
nums
except the last two, as we need at least three elements to form a triplet. - Return
closest_sum
, which holds the sum of the three integers closest to the target.
4. Explain your approach:
We will sort the array nums
to simplify the search for the closest sum. Then, we iterate through the array and use two pointers, left
and right
, to explore all possible combinations of three integers. We update the closest_sum
whenever we find a closer sum to the target. Finally, we return closest_sum
.
5. Write clean and readable code:
Here's an implementation of the algorithm in Python:
python
def threeSumClosest(nums, target):
nums.sort()
closest_sum = float('inf')
n = len(nums)
for i in range(n - 2):
left = i + 1
right = n - 1
while left < right:
current_sum = nums[i] + nums[left] + nums[right]
if abs(current_sum - target) < abs(closest_sum - target):
closest_sum = current_sum
if current_sum > target:
right -= 1
else:
left += 1
return closest_sum
6. Test your code: Let's test the code with some example test cases and additional cases:
python
# Example test case
nums = [-1, 2, 1, -4]
target = 1
closest_sum = threeSumClosest(nums, target)
# Expected output: 2
# Additional test cases
nums = [1, 1, 1, 0]
target = -100
closest_sum = threeSumClosest(nums, target)
# Expected output: 2 (1 + 1 + 0 = 2)
nums = [0, 0, 0]
target = 1
closest_sum = threeSumClosest(nums, target)
# Expected output: 0 (0 + 0 + 0 = 0)
nums = [4, -1, -4, 4]
target = 1
closest_sum = threeSumClosest(nums, target)
# Expected output: 1 (-1 + 4 + 4 = 9)
nums = [1, 2, 4, 8, 16, 32, 64, 128]
target = 82
closest_sum = threeSumClosest(nums, target)
# Expected output: 82 (32 + 16 + 32 = 82)
7. Optimize if necessary: The implemented algorithm already has a time complexity of O(n^2), where n is the length of the input array. It is already an optimal solution for this problem, so there is no further optimization required.
8. Handle error cases:
The given code assumes that the input array nums
will always have a length of at least 3. It does not handle the case of an empty array. Error handling strategies can be discussed with the interviewer.
9. Discuss complexity analysis:
- Time complexity: The algorithm has a time complexity of O(n^2), where n is the length of the input array
nums
. This is because we have two nested loops: one loop iterates through each element ofnums
, and the other loop iterates through the remaining elements using two pointers. - Space complexity: The space complexity is O(1) since the algorithm uses a constant amount of extra space to store variables.