018 四数相加

LeetCode 第十八题 四数相加

给定一个含有 n 个整数的数组 S，数列 S 中是否存在元素 a，b，c 和 d 使 a + b + c + d = target ？
请在数组中找出所有满足各元素相加等于特定值 的 不重复 组合。
注意：解决方案集不能包含重复的四元组合。
例如，给定数组 S = [1, 0, -1, 0, -2, 2]，并且给定 target = 0。

示例答案为：
[
[-1, 0, 0, 1],
[-2, -1, 1, 2],
[-2, 0, 0, 2]
]
其实这道题和第十五道题三数之和类似，在三数之和的解题步骤基础上再添加了一道循环，变成了本次题目的四数相加。
同时，为了节省时间，我们又在程序中添加了几个条件判断，如果不满足条件，不在做无畏的运算了。具体请参考代码。

Java

    public static List<List<Integer>> fourSum(int[] nums, int target) {
        List<List<Integer>> result = new LinkedList<>();
        Arrays.sort(nums);
        if (nums.length < 4)
            return result;
        int n = nums.length;
        for (int i = 0; i < n - 3; i++) {
            if (i > 0 && nums[i] == nums[i - 1])
                continue;/// 相同数字的跳过，节省时间
            if (nums[i] + nums[i + 1] + nums[i + 2] + nums[i + 3] > target)
                break;/// 不合理情况，直接返回，节省时间
            if (nums[i] + nums[n - 1] + nums[n - 2] + nums[n - 3] < target)
                continue;/// 跳过太小的数字，节省时间
            for (int j = i + 1; j < n - 2; j++) {
                if (j > i+1 && nums[j] == nums[j - 1])
                    continue;/// 同理
                if ((j + 2) < n && nums[i] + nums[j] + nums[j + 1] + nums[j + 2] > target)
                    break;
                if (nums[i] + nums[j] + nums[n - 1] + nums[n - 2] < target)
                    continue;
                int left = j + 1, right = n - 1;
                while (left < right) {
                    int current_sum = nums[i] + nums[j] + nums[left] + nums[right];
                    if (current_sum == target) {
                        result.add(Arrays.asList(nums[i], nums[j], nums[left], nums[right]));
                        while (left < right && nums[left] == nums[left + 1])
                            left++;
                        while (left < right && nums[right] == nums[right - 1])
                            right--;
                        left++;
                        right--;
                    } else if (current_sum < target) {
                        left++;
                    } else {
                        right--;
                    }
                }
            }
        }
        return result;
    }

C++

class Solution
{
public:
    vector<vector<int> > fourSum(vector<int>& nums,int target)
    {
        vector<vector<int> > result=vector<vector<int> >();
        if(nums.size()<4)return result;
        sort(nums.begin(),nums.end());
        int n = nums.size();
        for(int i=0; i<n-3; i++)
        {
            if(i>0&&nums[i]==nums[i-1])continue;
            if(nums[i]+nums[i+1]+nums[i+2]+nums[i+3]>target)break;
            if(nums[i]+nums[n-3]+nums[n-2]+nums[n-1]<target)continue;
            for(int j=i+1; j<n-2; j++)
            {
                if(j>i+1&&nums[j]==nums[j-1])continue;///一定是j>j+1而不是j>0 要确保第一个数字被检查
                if(nums[i]+nums[j]+nums[j+1]+nums[j+2]>target)break;
                if(nums[i]+nums[j]+nums[n-2]+nums[n-1]<target)continue;
                int low=j+1,high=n-1;
                while(low<high)
                {
                    int current_sum=nums[i]+nums[j]+nums[low]+nums[high];
                    if(current_sum==target)
                    {
                        vector<int>vec=vector<int>();
                        vec.push_back(nums[i]);
                        vec.push_back(nums[j]);
                        vec.push_back(nums[low]);
                        vec.push_back(nums[high]);
                        result.push_back(vec);
                        while(low<high&&nums[low]==nums[low+1])low++;
                        while(low<high&&nums[high]==nums[high-1])high--;
                        low++;
                        high--;
                    }
                    else if(current_sum<target)
                        low++;
                    else
                        high--;
                }
            }
        }


        return result;
    }
};

Python

class Solution(object):
    def fourSum(self, nums, target):
        result = []
        if len(nums) < 4:
            return result
        nums = sorted(nums)
        n = len(nums)
        for i in range(n - 3):
            if (i > 0 and nums[i] == nums[i - 1]): continue
            if (nums[i] + nums[i + 1] + nums[i + 2] + nums[i + 3] > target): break
            if (nums[i] + nums[n - 3] + nums[n - 2] + nums[n - 1] < target): continue
            for j in range(i + 1, n - 2):
                if (j > i + 1 and nums[j] == nums[j - 1]): continue
                if (nums[i] + nums[j] + nums[j + 1] + nums[j + 2] > target): break
                if (nums[i] + nums[j] + nums[n - 2] + nums[n - 1] < target): continue
                low, high = j + 1, n - 1
                while (low < high):
                    current_sum = nums[i] + nums[j] + nums[low] + nums[high]
                    if (current_sum == target):
                        result.append([nums[i], nums[j], nums[low], nums[high]])
                        while (low < high and nums[low] == nums[low + 1]): low = low + 1
                        while (low < high and nums[high] == nums[high - 1]): high = high - 1
                        low = low + 1
                        high = high - 1
                    elif current_sum < target:
                        low = low + 1
                    else:
                        high = high - 1
        return result