Description#
Given an array nums of n integers, return an array of all the unique quadruplets [nums[a], nums[b], nums[c], nums[d]] such that:
0 <= a, b, c, d < na, b, c, and d are distinct.nums[a] + nums[b] + nums[c] + nums[d] == target
You may return the answer in any order.
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]]
Constraints:
1 <= nums.length <= 200-109 <= nums[i] <= 109-109 <= target <= 109
Solutions#
Solution 1: Sorting + Double Pointers#
We notice that the problem requires us to find non-repeating quadruplets. Therefore, we can first sort the array, which makes it easy to skip duplicate elements.
Next, we enumerate the first two elements of the quadruplet, $nums[i]$ and $nums[j]$, where $i \lt j$. During the enumeration process, we skip duplicate $nums[i]$ and $nums[j]$. Then, we use two pointers $k$ and $l$ to point to the two ends behind $nums[i]$ and $nums[j]$. Let $x = nums[i] + nums[j] + nums[k] + nums[l]$, we compare $x$ with $target$ and perform the following operations:
- If $x \lt target$, then update $k = k + 1$ to get a larger $x$;
- If $x \gt target$, then update $l = l - 1$ to get a smaller $x$;
- Otherwise, it means that a quadruplet $(nums[i], nums[j], nums[k], nums[l])$ is found. Add it to the answer, then we update the pointers $k$ and $l$, and skip all duplicate elements to prevent the answer from containing duplicate quadruplets, and continue to find the next quadruplet.
The time complexity is $O(n^3)$, and the space complexity is $O(\log n)$. Here, $n$ is the length of the array.
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| class Solution:
def fourSum(self, nums: List[int], target: int) -> List[List[int]]:
n = len(nums)
ans = []
if n < 4:
return ans
nums.sort()
for i in range(n - 3):
if i 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
k, l = j + 1, n - 1
while k < l:
x = nums[i] + nums[j] + nums[k] + nums[l]
if x < target:
k += 1
elif x > target:
l -= 1
else:
ans.append([nums[i], nums[j], nums[k], nums[l]])
k, l = k + 1, l - 1
while k < l and nums[k] == nums[k - 1]:
k += 1
while k < l and nums[l] == nums[l + 1]:
l -= 1
return ans
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| class Solution {
public List<List<Integer>> fourSum(int[] nums, int target) {
int n = nums.length;
List<List<Integer>> ans = new ArrayList<>();
if (n < 4) {
return ans;
}
Arrays.sort(nums);
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 k = j + 1, l = n - 1;
while (k < l) {
long x = (long) nums[i] + nums[j] + nums[k] + nums[l];
if (x < target) {
++k;
} else if (x > target) {
--l;
} else {
ans.add(List.of(nums[i], nums[j], nums[k++], nums[l--]));
while (k < l && nums[k] == nums[k - 1]) {
++k;
}
while (k < l && nums[l] == nums[l + 1]) {
--l;
}
}
}
}
}
return ans;
}
}
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| class Solution {
public:
vector<vector<int>> fourSum(vector<int>& nums, int target) {
int n = nums.size();
vector<vector<int>> ans;
if (n < 4) {
return ans;
}
sort(nums.begin(), nums.end());
for (int i = 0; i < n - 3; ++i) {
if (i && 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 k = j + 1, l = n - 1;
while (k < l) {
long long x = (long long) nums[i] + nums[j] + nums[k] + nums[l];
if (x < target) {
++k;
} else if (x > target) {
--l;
} else {
ans.push_back({nums[i], nums[j], nums[k++], nums[l--]});
while (k < l && nums[k] == nums[k - 1]) {
++k;
}
while (k < l && nums[l] == nums[l + 1]) {
--l;
}
}
}
}
}
return ans;
}
};
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| func fourSum(nums []int, target int) (ans [][]int) {
n := len(nums)
if n < 4 {
return
}
sort.Ints(nums)
for i := 0; i < n-3; i++ {
if i > 0 && nums[i] == nums[i-1] {
continue
}
for j := i + 1; j < n-2; j++ {
if j > i+1 && nums[j] == nums[j-1] {
continue
}
k, l := j+1, n-1
for k < l {
x := nums[i] + nums[j] + nums[k] + nums[l]
if x < target {
k++
} else if x > target {
l--
} else {
ans = append(ans, []int{nums[i], nums[j], nums[k], nums[l]})
k++
l--
for k < l && nums[k] == nums[k-1] {
k++
}
for k < l && nums[l] == nums[l+1] {
l--
}
}
}
}
}
return
}
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| function fourSum(nums: number[], target: number): number[][] {
const n = nums.length;
const ans: number[][] = [];
if (n < 4) {
return ans;
}
nums.sort((a, b) => a - b);
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 [k, l] = [j + 1, n - 1];
while (k < l) {
const x = nums[i] + nums[j] + nums[k] + nums[l];
if (x < target) {
++k;
} else if (x > target) {
--l;
} else {
ans.push([nums[i], nums[j], nums[k++], nums[l--]]);
while (k < l && nums[k] === nums[k - 1]) {
++k;
}
while (k < l && nums[l] === nums[l + 1]) {
--l;
}
}
}
}
}
return ans;
}
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| /**
* @param {number[]} nums
* @param {number} target
* @return {number[][]}
*/
var fourSum = function (nums, target) {
const n = nums.length;
const ans = [];
if (n < 4) {
return ans;
}
nums.sort((a, b) => a - b);
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 [k, l] = [j + 1, n - 1];
while (k < l) {
const x = nums[i] + nums[j] + nums[k] + nums[l];
if (x < target) {
++k;
} else if (x > target) {
--l;
} else {
ans.push([nums[i], nums[j], nums[k++], nums[l--]]);
while (k < l && nums[k] === nums[k - 1]) {
++k;
}
while (k < l && nums[l] === nums[l + 1]) {
--l;
}
}
}
}
}
return ans;
};
|
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| public class Solution {
public IList<IList<int>> FourSum(int[] nums, int target) {
int n = nums.Length;
var ans = new List<IList<int>>();
if (n < 4) {
return ans;
}
Array.Sort(nums);
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 k = j + 1, l = n - 1;
while (k < l) {
long x = (long) nums[i] + nums[j] + nums[k] + nums[l];
if (x < target) {
++k;
} else if (x > target) {
--l;
} else {
ans.Add(new List<int> {nums[i], nums[j], nums[k++], nums[l--]});
while (k < l && nums[k] == nums[k - 1]) {
++k;
}
while (k < l && nums[l] == nums[l + 1]) {
--l;
}
}
}
}
}
return ans;
}
}
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