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 length n and an integer target.
  • Output: The sum of three integers from nums that is closest to the target.
  • 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:

  1. Sort the array nums in non-decreasing order.
  2. Initialize a variable closest_sum to store the closest sum found so far. Set it to a large value initially.
  3. 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 and right, 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 between current_sum and target is smaller than the absolute difference between closest_sum and target.
    • If current_sum is greater than target, decrement right to try a smaller value. Otherwise, increment left to try a larger value.
  4. Repeat the above steps for all elements of nums except the last two, as we need at least three elements to form a triplet.
  5. 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 of nums, 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.
Next Post Previous Post