Skip to content

16. 3Sum Closest

Description

Given an integer array nums of length n and an integer target, find three integers at distinct indices in nums such that the sum is closest to target.

Return the sum of the three integers.

You may assume that each input would have exactly one solution.

 

Example 1:

Input: nums = [-1,2,1,-4], target = 1
Output: 2
Explanation: The sum that is closest to the target is 2. (-1 + 2 + 1 = 2).

Example 2:

Input: nums = [0,0,0], target = 1
Output: 0
Explanation: The sum that is closest to the target is 0. (0 + 0 + 0 = 0).

 

Constraints:

  • 3 <= nums.length <= 500
  • -1000 <= nums[i] <= 1000
  • -104 <= target <= 104

Solutions

Solution 1: Sorting + Two Pointers

Thinking

The first idea is to try every triplet and keep the sum closest to \(target\). That is \(O(n^3)\). \(n\le 1000\) is about \(10^9\) operations and will not pass.

The bottleneck is still brute-forcing the other two numbers after fixing one. We do not need every triplet, only the sum nearest \(target\). After sorting, a sum that is too large can only get closer by moving the right end left; one that is too small must move the left end right. An exact hit is already optimal.

So we enumerate the first number and squeeze the rest with two pointers, tracking the smallest deviation. The answer is unique, so we need not skip duplicates.

We sort the array first, then traverse the array. For each element \(nums[i]\), we use pointers \(j\) and \(k\) to point to \(i+1\) and \(n-1\) respectively, calculate the sum of the three numbers. If the sum of the three numbers equals \(target\), we directly return \(target\). Otherwise, we update the answer based on the difference from \(target\). If the sum of the three numbers is greater than \(target\), we move \(k\) one place to the left, otherwise, we move \(j\) one place to the right.

The time complexity is \(O(n^2)\), and the space complexity is \(O(\log n)\). Here, \(n\) is the length of the array.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
class Solution:
    def threeSumClosest(self, nums: List[int], target: int) -> int:
        nums.sort()
        n = len(nums)
        ans = inf
        for i, v in enumerate(nums):
            j, k = i + 1, n - 1
            while j < k:
                t = v + nums[j] + nums[k]
                if t == target:
                    return t
                if abs(t - target) < abs(ans - target):
                    ans = t
                if t > target:
                    k -= 1
                else:
                    j += 1
        return ans

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
class Solution {
    public int threeSumClosest(int[] nums, int target) {
        Arrays.sort(nums);
        int ans = 1 << 30;
        int n = nums.length;
        for (int i = 0; i < n; ++i) {
            int j = i + 1, k = n - 1;
            while (j < k) {
                int t = nums[i] + nums[j] + nums[k];
                if (t == target) {
                    return t;
                }
                if (Math.abs(t - target) < Math.abs(ans - target)) {
                    ans = t;
                }
                if (t > target) {
                    --k;
                } else {
                    ++j;
                }
            }
        }
        return ans;
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
class Solution {
public:
    int threeSumClosest(vector<int>& nums, int target) {
        sort(nums.begin(), nums.end());
        int ans = 1 << 30;
        int n = nums.size();
        for (int i = 0; i < n; ++i) {
            int j = i + 1, k = n - 1;
            while (j < k) {
                int t = nums[i] + nums[j] + nums[k];
                if (t == target) return t;
                if (abs(t - target) < abs(ans - target)) ans = t;
                if (t > target)
                    --k;
                else
                    ++j;
            }
        }
        return ans;
    }
};

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
func threeSumClosest(nums []int, target int) int {
    sort.Ints(nums)
    ans := 1 << 30
    n := len(nums)
    for i, v := range nums {
        j, k := i+1, n-1
        for j < k {
            t := v + nums[j] + nums[k]
            if t == target {
                return t
            }
            if abs(t-target) < abs(ans-target) {
                ans = t
            }
            if t > target {
                k--
            } else {
                j++
            }
        }
    }
    return ans
}

func abs(x int) int {
    if x < 0 {
        return -x
    }
    return x
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
function threeSumClosest(nums: number[], target: number): number {
    nums.sort((a, b) => a - b);
    let ans: number = 1 << 30;
    const n = nums.length;
    for (let i = 0; i < n; ++i) {
        let j = i + 1;
        let k = n - 1;
        while (j < k) {
            const t: number = nums[i] + nums[j] + nums[k];
            if (t === target) {
                return t;
            }
            if (Math.abs(t - target) < Math.abs(ans - target)) {
                ans = t;
            }
            if (t > target) {
                --k;
            } else {
                ++j;
            }
        }
    }
    return ans;
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
/**
 * @param {number[]} nums
 * @param {number} target
 * @return {number}
 */
var threeSumClosest = function (nums, target) {
    nums.sort((a, b) => a - b);
    let ans = 1 << 30;
    const n = nums.length;
    for (let i = 0; i < n; ++i) {
        let j = i + 1;
        let k = n - 1;
        while (j < k) {
            const t = nums[i] + nums[j] + nums[k];
            if (t === target) {
                return t;
            }
            if (Math.abs(t - target) < Math.abs(ans - target)) {
                ans = t;
            }
            if (t > target) {
                --k;
            } else {
                ++j;
            }
        }
    }
    return ans;
};

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
public class Solution {
    public int ThreeSumClosest(int[] nums, int target) {
        Array.Sort(nums);
        int ans = 1 << 30;
        int n = nums.Length;
        for (int i = 0; i < n; ++i) {
            int j = i + 1, k = n - 1;
            while (j < k) {
                int t = nums[i] + nums[j] + nums[k];
                if (t == target) {
                    return t;
                }
                if (Math.Abs(t - target) < Math.Abs(ans - target)) {
                    ans = t;
                }
                if (t > target) {
                    --k;
                } else {
                    ++j;
                }
            }
        }
        return ans;
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
class Solution {
    /**
     * @param int[] $nums
     * @param int $target
     * @return int
     */

    function threeSumClosest($nums, $target) {
        $n = count($nums);
        $closestSum = $nums[0] + $nums[1] + $nums[2];
        $minDiff = abs($closestSum - $target);

        sort($nums);

        for ($i = 0; $i < $n - 2; $i++) {
            $left = $i + 1;
            $right = $n - 1;

            while ($left < $right) {
                $sum = $nums[$i] + $nums[$left] + $nums[$right];
                $diff = abs($sum - $target);

                if ($diff < $minDiff) {
                    $minDiff = $diff;
                    $closestSum = $sum;
                } elseif ($sum < $target) {
                    $left++;
                } elseif ($sum > $target) {
                    $right--;
                } else {
                    return $sum;
                }
            }
        }

        return $closestSum;
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
int cmp(const void* a, const void* b) {
    return (*(int*) a - *(int*) b);
}

int threeSumClosest(int* nums, int numsSize, int target) {
    qsort(nums, numsSize, sizeof(int), cmp);
    int ans = 1 << 30;
    for (int i = 0; i < numsSize; ++i) {
        int j = i + 1, k = numsSize - 1;
        while (j < k) {
            int t = nums[i] + nums[j] + nums[k];
            if (t == target) {
                return t;
            }
            if (abs(t - target) < abs(ans - target)) {
                ans = t;
            }
            if (t > target) {
                --k;
            } else {
                ++j;
            }
        }
    }
    return ans;
}

Comments