[LeetCode] 16. 3Sum Closest 最近三数之和

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

Example:

Given array nums = [-1, 2, 1, -4], and target = 1.

The sum that is closest to the target is 2. (-1 + 2 + 1 = 2).

这道题让我们求最接近给定值的三数之和，是在之前那道 3Sum 的基础上又增加了些许难度，那么这道题让返回这个最接近于给定值的值，即要保证当前三数和跟给定值之间的差的绝对值最小，所以需要定义一个变量 diff 用来记录差的绝对值，然后还是要先将数组排个序，然后开始遍历数组，思路跟那道三数之和很相似，都是先确定一个数，然后用两个指针 left 和 right 来滑动寻找另外两个数，每确定两个数，求出此三数之和，然后算和给定值的差的绝对值存在 newDiff 中，然后和 diff 比较并更新 diff 和结果 closest 即可，代码如下：

解法一：

class Solution {
public:
    int threeSumClosest(vector<int>& nums, int target) {
        int closest = nums[0] + nums[1] + nums[2];
        int diff = abs(closest - target);
        sort(nums.begin(), nums.end());
        for (int i = 0; i < nums.size() - 2; ++i) {
            int left = i + 1, right = nums.size() - 1;
            while (left < right) {
                int sum = nums[i] + nums[left] + nums[right];
                int newDiff = abs(sum - target);
                if (diff > newDiff) {
                    diff = newDiff;
                    closest = sum;
                }
                if (sum < target) ++left;
                else --right;
            }
        }
        return closest;
    }
};

我们还可以稍稍进行一下优化，每次判断一下，当 nums[i]*3 > target 的时候，就可以直接比较 closest 和 nums[i] + nums[i+1] + nums[i+2] 的值，返回较小的那个，因为数组已经排过序了，后面的数字只会越来越大，就不必再往后比较了，参见代码如下：

解法二：

class Solution {
public:
    int threeSumClosest(vector<int>& nums, int target) {
        int closest = nums[0] + nums[1] + nums[2];
        int diff = abs(closest - target);
        sort(nums.begin(), nums.end());
        for (int i = 0; i < nums.size() - 2; ++i) {
            if (nums[i] * 3 > target) return min(closest, nums[i] + nums[i + 1] + nums[i + 2]);
            int left = i + 1, right = nums.size() - 1;
            while (left < right) {
                int sum = nums[i] + nums[left] + nums[right];
                int newDiff = abs(sum - target);
                if (diff > newDiff) {
                    diff = newDiff;
                    closest = sum;
                }
                if (sum < target) ++left;
                else --right;
            }
        }
        return closest;
    }
};

Github 同步地址：

https://github.com/grandyang/leetcode/issues/16

类似题目：

3Sum Smaller

3Sum

参考资料：

https://leetcode.com/problems/3sum-closest/

https://leetcode.com/problems/3sum-closest/discuss/7883/C%2B%2B-solution-O(n2)-using-sort

https://leetcode.com/problems/3sum-closest/discuss/7872/Java-solution-with-O(n2)-for-reference

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