4Sum

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

For example, given array S = [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]]

这道题刚开始是用3Sum那道题的思想去写的，但是却TimeLimited，不过可以放在这里供自己和他人去看这个算法的思想。

public class Solution {    public List<List<Integer>> fourSum(int[] nums, int target){List<List<Integer>> result = new ArrayList<List<Integer>>();Arrays.sort(nums);for (int i = 0; i < nums.length - 3; i++){for (int j = i + 1; j < nums.length - 2; j++){int l = j + 1;int r = nums.length - 1;while (l < r){int sum = nums[i] + nums[j] + nums[l] + nums[r];if (sum == target){    List<Integer> group = new ArrayList<>();group.add(nums[i]);group.add(nums[j]);group.add(nums[l]);group.add(nums[r]);result.add(group);l++;r--;while (l < r){if (nums[l] == nums[l - 1])l++;if (nums[r] == nums[r - 1])r--;}}else if (sum < target){l++;}else{r--;}}}}return result;}}

后来去讨论区参考了一下别人的代码，想法确实挺新颖的：

package com.alibaba.learning;import java.util.ArrayList;import java.util.Arrays;import java.util.List;public class Solution{public List<List<Integer>> fourSum(int[] nums, int target){ArrayList<List<Integer>> res = new ArrayList<>();int len = nums.length;if (nums == null || nums.length < 4)return res;Arrays.sort(nums);int max = nums[len - 1];if (4 * nums[0] > target || 4 * max < target)return res;int i, z;for (i = 0; i < len; i++){z = nums[i];if (i > 0 && z == nums[i - 1]) // 排除相同元素 保持输出结果元素的唯一性continue;if (z + 3 * max < target)continue;if (4 * z > target)break;if (4 * z == target) // z是临界值{if (i + 3 < len && nums[i + 3] == z)res.add(Arrays.asList(z, z, z, z));break;}threeSumForFourSum(nums, target - z, i + 1, len - 1, res, z);}return res;}public void threeSumForFourSum(int[] nums, int target, int low, int high, ArrayList<List<Integer>> fourSumList,int z1){if (low + 1 >= high)return;int max = nums[high];if (3 * nums[low] > target || 3 * nums[high] < target)return;int i, z;for (i = low; i < high - 1; i++){z = nums[i];if (i > low && z == nums[i - 1])continue;if (z + 2 * max < target)continue;if (3 * z > target)break;if (3 * z == target){if (i + 1 < high && nums[i + 2] == z)fourSumList.add(Arrays.asList(z, z, z));break;}twoSumForFourSum(nums, target - z, i + 1, high, fourSumList, z1, z);}}public void twoSumForFourSum(int[] nums, int target, int low, int high, ArrayList<List<Integer>> fourSumList,int z1, int z2){if (low >= high)return;if (2 * nums[low] > target || 2 * nums[high] < target)return;int i = low, j = high, sum, x;while (i < j){sum = nums[i] + nums[j];if (sum == target){fourSumList.add(Arrays.asList(z1, z2, nums[i], nums[j]));x = nums[i];while (++i < j && x == nums[i]) // avoid duplicate;x = nums[j];while (i < --j && x == nums[j]) // avoid duplicate;}if (sum < target)i++;if (sum > target)j--;}return;}}