18. 4Sum

Medium

Problem Description

Given an array nums of n integers and an integer target, find all unique quadruplets in the array which gives the sum of target. Return the answer in any order.

Examples

Example 1:
Input: nums = [1,0,-1,0,-2,2], target = 0
Output: [[-2,-1,1,2],[-2,0,0,2],[-1,0,0,1]]

Example 2:
Input: nums = [2,2,2,2,2], target = 8
Output: [[2,2,2,2]]
Jump to Solution: Python Java C++ JavaScript C#

Solutions

Python Solution


def fourSum(nums: List[int], target: int) -> List[List[int]]:
    nums.sort()
    n = len(nums)
    result = []
    
    for i in range(n - 3):
        if i > 0 and nums[i] == nums[i - 1]:
            continue
            
        for j in range(i + 1, n - 2):
            if j > i + 1 and nums[j] == nums[j - 1]:
                continue
                
            left = j + 1
            right = n - 1
            
            while left < right:
                curr_sum = nums[i] + nums[j] + nums[left] + nums[right]
                
                if curr_sum == target:
                    result.append([nums[i], nums[j], nums[left], nums[right]])
                    while left < right and nums[left] == nums[left + 1]:
                        left += 1
                    while left < right and nums[right] == nums[right - 1]:
                        right -= 1
                    left += 1
                    right -= 1
                elif curr_sum < target:
                    left += 1
                else:
                    right -= 1
    
    return result
    

Java Solution


class Solution {
    public List> fourSum(int[] nums, int target) {
        Arrays.sort(nums);
        List> result = new ArrayList<>();
        int n = nums.length;
        
        for (int i = 0; i < n - 3; i++) {
            if (i > 0 && nums[i] == nums[i - 1]) continue;
            
            for (int j = i + 1; j < n - 2; j++) {
                if (j > i + 1 && nums[j] == nums[j - 1]) continue;
                
                int left = j + 1;
                int right = n - 1;
                
                while (left < right) {
                    long sum = (long)nums[i] + nums[j] + nums[left] + nums[right];
                    
                    if (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 (sum < target) {
                        left++;
                    } else {
                        right--;
                    }
                }
            }
        }
        
        return result;
    }
}
    

C++ Solution


class Solution {
public:
    vector> fourSum(vector& nums, int target) {
        sort(nums.begin(), nums.end());
        vector> result;
        int n = nums.size();
        
        for (int i = 0; i < n - 3; i++) {
            if (i > 0 && nums[i] == nums[i - 1]) continue;
            
            for (int j = i + 1; j < n - 2; j++) {
                if (j > i + 1 && nums[j] == nums[j - 1]) continue;
                
                int left = j + 1;
                int right = n - 1;
                
                while (left < right) {
                    long long sum = (long long)nums[i] + nums[j] + nums[left] + nums[right];
                    
                    if (sum == target) {
                        result.push_back({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 (sum < target) {
                        left++;
                    } else {
                        right--;
                    }
                }
            }
        }
        
        return result;
    }
};
    

JavaScript Solution


/**
 * @param {number[]} nums
 * @param {number} target
 * @return {number[][]}
 */
var fourSum = function(nums, target) {
    nums.sort((a, b) => a - b);
    const result = [];
    const n = nums.length;
    
    for (let i = 0; i < n - 3; i++) {
        if (i > 0 && nums[i] === nums[i - 1]) continue;
        
        for (let j = i + 1; j < n - 2; j++) {
            if (j > i + 1 && nums[j] === nums[j - 1]) continue;
            
            let left = j + 1;
            let right = n - 1;
            
            while (left < right) {
                const sum = nums[i] + nums[j] + nums[left] + nums[right];
                
                if (sum === target) {
                    result.push([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 (sum < target) {
                    left++;
                } else {
                    right--;
                }
            }
        }
    }
    
    return result;
};
    

C# Solution


public class Solution {
    public IList> FourSum(int[] nums, int target) {
        Array.Sort(nums);
        var result = new List>();
        int n = nums.Length;
        
        for (int i = 0; i < n - 3; i++) {
            if (i > 0 && nums[i] == nums[i - 1]) continue;
            
            for (int j = i + 1; j < n - 2; j++) {
                if (j > i + 1 && nums[j] == nums[j - 1]) continue;
                
                int left = j + 1;
                int right = n - 1;
                
                while (left < right) {
                    long sum = (long)nums[i] + nums[j] + nums[left] + nums[right];
                    
                    if (sum == target) {
                        result.Add(new List { 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 (sum < target) {
                        left++;
                    } else {
                        right--;
                    }
                }
            }
        }
        
        return result;
    }
}
    

Complexity Analysis

Solution Explanation

This solution extends the 3Sum approach using sorting and two pointers. Here's how it works:

Key points: