4Sum(四数之和) – 每天一道算法题

题目 #

Given an array nums of n integers and an integer target, are there elements a, b, c, and d in nums such that a + b + c + d = target? Find all unique quadruplets in the array which gives the sum of target.

Note:

The solution set must not contain duplicate quadruplets.

Example:


Given array nums = [1, 0, -1, 0, -2, 2], and target = 0.

A solution set is:
[
  [-1,  0, 0, 1],
  [-2, -1, 1, 2],
  [-2,  0, 0, 2]
]

题目大意 #

给定一个数组,要求在这个数组中找出 4 个数之和为 0 的所有组合。

解题思路 #

用 map 提前计算好任意 3 个数字之和,保存起来,可以将时间复杂度降到 O(n^3)。这一题比较麻烦的一点在于,最后输出解的时候,要求输出不重复的解。数组中同一个数字可能出现多次,同一个数字也可能使用多次,但是最后输出解的时候,不能重复。例如 [-1,1,2, -2] 和 [2, -1, -2, 1]、[-2, 2, -1, 1] 这 3 个解是重复的,即使 -1, -2 可能出现 100 次,每次使用的 -1, -2 的数组下标都是不同的。

这一题是第 15 题的升级版,思路都是完全一致的。这里就需要去重和排序了。map 记录每个数字出现的次数,然后对 map 的 key 数组进行排序,最后在这个排序以后的数组里面扫,找到另外 3 个数字能和自己组成 0 的组合。

第 15 题和第 18 题的解法一致。

Go代码 #

package leetcode

import "sort"

// 解法一 双指针
func fourSum(nums []int, target int) (quadruplets [][]int) {
	sort.Ints(nums)
	n := len(nums)
	for i := 0; i < n-3 && nums[i]+nums[i+1]+nums[i+2]+nums[i+3] <= target; i++ {
		if i > 0 && nums[i] == nums[i-1] || nums[i]+nums[n-3]+nums[n-2]+nums[n-1] < target {
			continue
		}
		for j := i + 1; j < n-2 && nums[i]+nums[j]+nums[j+1]+nums[j+2] <= target; j++ {
			if j > i+1 && nums[j] == nums[j-1] || nums[i]+nums[j]+nums[n-2]+nums[n-1] < target {
				continue
			}
			for left, right := j+1, n-1; left < right; {
				if sum := nums[i] + nums[j] + nums[left] + nums[right]; sum == target {
					quadruplets = append(quadruplets, []int{nums[i], nums[j], nums[left], nums[right]})
					for left++; left < right && nums[left] == nums[left-1]; left++ {
					}
					for right--; left < right && nums[right] == nums[right+1]; right-- {
					}
				} else if sum < target {
					left++
				} else {
					right--
				}
			}
		}
	}
	return
}

// 解法二 kSum
func fourSum1(nums []int, target int) [][]int {
	res, cur := make([][]int, 0), make([]int, 0)
	sort.Ints(nums)
	kSum(nums, 0, len(nums)-1, target, 4, cur, &res)
	return res
}

func kSum(nums []int, left, right int, target int, k int, cur []int, res *[][]int) {
	if right-left+1 < k || k < 2 || target < nums[left]*k || target > nums[right]*k {
		return
	}
	if k == 2 {
		// 2 sum
		twoSum(nums, left, right, target, cur, res)
	} else {
		for i := left; i < len(nums); i++ {
			if i == left || (i > left && nums[i-1] != nums[i]) {
				next := make([]int, len(cur))
				copy(next, cur)
				next = append(next, nums[i])
				kSum(nums, i+1, len(nums)-1, target-nums[i], k-1, next, res)
			}
		}
	}

}

func twoSum(nums []int, left, right int, target int, cur []int, res *[][]int) {
	for left < right {
		sum := nums[left] + nums[right]
		if sum == target {
			cur = append(cur, nums[left], nums[right])
			temp := make([]int, len(cur))
			copy(temp, cur)
			*res = append(*res, temp)
			// reset cur to previous state
			cur = cur[:len(cur)-2]
			left++
			right--
			for left < right && nums[left] == nums[left-1] {
				left++
			}
			for left < right && nums[right] == nums[right+1] {
				right--
			}
		} else if sum < target {
			left++
		} else {
			right--
		}
	}
}

// 解法三
func fourSum2(nums []int, target int) [][]int {
	res := [][]int{}
	counter := map[int]int{}
	for _, value := range nums {
		counter[value]++
	}

	uniqNums := []int{}
	for key := range counter {
		uniqNums = append(uniqNums, key)
	}
	sort.Ints(uniqNums)

	for i := 0; i < len(uniqNums); i++ {
		if (uniqNums[i]*4 == target) && counter[uniqNums[i]] >= 4 {
			res = append(res, []int{uniqNums[i], uniqNums[i], uniqNums[i], uniqNums[i]})
		}
		for j := i + 1; j < len(uniqNums); j++ {
			if (uniqNums[i]*3+uniqNums[j] == target) && counter[uniqNums[i]] > 2 {
				res = append(res, []int{uniqNums[i], uniqNums[i], uniqNums[i], uniqNums[j]})
			}
			if (uniqNums[j]*3+uniqNums[i] == target) && counter[uniqNums[j]] > 2 {
				res = append(res, []int{uniqNums[i], uniqNums[j], uniqNums[j], uniqNums[j]})
			}
			if (uniqNums[j]*2+uniqNums[i]*2 == target) && counter[uniqNums[j]] > 1 && counter[uniqNums[i]] > 1 {
				res = append(res, []int{uniqNums[i], uniqNums[i], uniqNums[j], uniqNums[j]})
			}
			for k := j + 1; k < len(uniqNums); k++ {
				if (uniqNums[i]*2+uniqNums[j]+uniqNums[k] == target) && counter[uniqNums[i]] > 1 {
					res = append(res, []int{uniqNums[i], uniqNums[i], uniqNums[j], uniqNums[k]})
				}
				if (uniqNums[j]*2+uniqNums[i]+uniqNums[k] == target) && counter[uniqNums[j]] > 1 {
					res = append(res, []int{uniqNums[i], uniqNums[j], uniqNums[j], uniqNums[k]})
				}
				if (uniqNums[k]*2+uniqNums[i]+uniqNums[j] == target) && counter[uniqNums[k]] > 1 {
					res = append(res, []int{uniqNums[i], uniqNums[j], uniqNums[k], uniqNums[k]})
				}
				c := target - uniqNums[i] - uniqNums[j] - uniqNums[k]
				if c > uniqNums[k] && counter[c] > 0 {
					res = append(res, []int{uniqNums[i], uniqNums[j], uniqNums[k], c})
				}
			}
		}
	}
	return res
}

java代码 #

class Solution {
    public List<List<Integer>> fourSum(int[] nums, int target) {
        List<List<Integer>> quadruplets = new ArrayList<List<Integer>>();
        if (nums == null || nums.length < 4) {
            return quadruplets;
        }
        Arrays.sort(nums);
        int length = nums.length;
        for (int i = 0; i < length - 3; i++) {
            if (i > 0 && nums[i] == nums[i - 1]) {
                continue;
            }
            if ((long) nums[i] + nums[i + 1] + nums[i + 2] + nums[i + 3] > target) {
                break;
            }
            if ((long) nums[i] + nums[length - 3] + nums[length - 2] + nums[length - 1] < target) {
                continue;
            }
            for (int j = i + 1; j < length - 2; j++) {
                if (j > i + 1 && nums[j] == nums[j - 1]) {
                    continue;
                }
                if ((long) nums[i] + nums[j] + nums[j + 1] + nums[j + 2] > target) {
                    break;
                }
                if ((long) nums[i] + nums[j] + nums[length - 2] + nums[length - 1] < target) {
                    continue;
                }
                int left = j + 1, right = length - 1;
                while (left < right) {
                    int sum = nums[i] + nums[j] + nums[left] + nums[right];
                    if (sum == target) {
                        quadruplets.add(Arrays.asList(nums[i], nums[j], nums[left], nums[right]));
                        while (left < right && nums[left] == nums[left + 1]) {
                            left++;
                        }
                        left++;
                        while (left < right && nums[right] == nums[right - 1]) {
                            right--;
                        }
                        right--;
                    } else if (sum < target) {
                        left++;
                    } else {
                        right--;
                    }
                }
            }
        }
        return quadruplets;
    }
}

python代码 #

class Solution:
    def fourSum(self, nums: List[int], target: int) -> List[List[int]]:
        quadruplets = list()
        if not nums or len(nums) < 4:
            return quadruplets
        
        nums.sort()
        length = len(nums)
        for i in range(length - 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[length - 3] + nums[length - 2] + nums[length - 1] < target:
                continue
            for j in range(i + 1, length - 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[length - 2] + nums[length - 1] < target:
                    continue
                left, right = j + 1, length - 1
                while left < right:
                    total = nums[i] + nums[j] + nums[left] + nums[right]
                    if total == target:
                        quadruplets.append([nums[i], nums[j], nums[left], nums[right]])
                        while left < right and nums[left] == nums[left + 1]:
                            left += 1
                        left += 1
                        while left < right and nums[right] == nums[right - 1]:
                            right -= 1
                        right -= 1
                    elif total < target:
                        left += 1
                    else:
                        right -= 1
        
        return quadruplets

 

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