/*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.

Note: The solution set must not contain duplicate quadruplets.

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]

]*/

public List<List<Integer>> fourSum(int[] nums, int target){

ArrayList<List<Integer>> res = new ArrayList<List<Integer>>();

int len = nums.length;

if(nums == null || len < 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]) continue;//avoid duplicate

if(z + 3 * max < target) continue;//z is too small

if(4 * z > target) break;

if(4 * z == target){//z is the boundary

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;

}

/*

Find all posible distinguished three numbers adding up to the target in sorted array nums[] between indices low and high. If there are, add all of them into the ArrayList fourSumList, using fourSumList.add(Arrays.asList(z1, the three numbers))

*/

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 * max < 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(z1, z, z, z));

break;

}

twoSumForFourSum(nums, target - z, i + 1, high, fourSumList, z1, z);

}

}

/*

Find all posible distinguished two numbers adding up to the target in sorted array nums[] between indices low and high. If there are, add all of them into the ArrayList fourSumList, using fourSumList.add(Arrays.asList(z1, z2, the two numbers)).

*/

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]);

x = nums[j];

while(i < --j && x == nums[j]);

}

if(sum < target) i++;

if(sum > target) j--;

}

return;

}