Question

18. 4Sum

中文文档

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 < n
• a, 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.

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

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;
  }
}

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;
  }
};

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
}

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;
}

/**
 * @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;
};

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;
  }
}

class Solution {
  /**
   * @param int[] $nums
   * @param int $target
   * @return int[][]
   */

  function fourSum($nums, $target) {
    $result = [];
    $n = count($nums);

    sort($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;
        }

        $left = $j + 1;
        $right = $n - 1;

        while ($left < $right) {
          $sum = $nums[$i] + $nums[$j] + $nums[$left] + $nums[$right];

          if ($sum === $target) {
            $result[] = [$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++;
            $right--;
          } elseif ($sum < $target) {
            $left++;
          } else {
            $right--;
          }
        }
      }
    }
    return $result;
  }
}