Find four elements that sum to a given value | Two-Pointer approach

Difficulty Level : Hard
Last Updated : 06 Apr, 2020

Given an array arr of integers of size N and a target number, the task is to find all unique quadruplets in it, whose sum is equal to the target number.

Examples:

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Input: arr[] = {4, 1, 2, -1, 1, -3], target = 1
Output: [[-3, -1, 1, 4], [-3, 1, 1, 2]]
Explanation:
Both the quadruplets sum equals to target.

Input: arr[] = {2, 0, -1, 1, -2, 2}, target = 2
Output: [[-2, 0, 2, 2], [-1, 0, 1, 2]]

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Two-Pointers approach:
This problem follows the Two Pointers pattern and shares similarities with Triplet Sum to Zero.

We can follow a similar approach to iterate through the array, taking one number at a time. At every step during the iteration, we will search for the quadruplets similar to Triplet Sum to Zero whose sum is equal to the given target.

C++

// C++ program to find four
// elements that sum to a given value
  
#include <bits/stdc++.h>
using namespace std;
  
class QuadrupleSumToTarget {
  
public:
    // Function to find quadruplets
    static vector<vector<int> >
    searchQuadruplets(
        vector<int>& arr,
        int target)
    {
        sort(arr.begin(), arr.end());
        vector<vector<int> > quadruplets;
  
        for (int i = 0; i < arr.size() - 3; i++) {
            if (i > 0 && arr[i] == arr[i - 1]) {
  
                // Skip same element
                // to avoid duplicate
                continue;
            }
  
            for (int j = i + 1; j < arr.size() - 2; j++) {
                if (j > i + 1 && arr[j] == arr[j - 1]) {
  
                    // Skip same element
                    // to avoid duplicate quad
                    continue;
                }
                searchPairs(
                    arr, target,
                    i, j, quadruplets);
            }
        }
        return quadruplets;
    }
  
private:
    // Function to search Quadruplets
    static void
    searchPairs(
        const vector<int>& arr,
        int targetSum, int first,
        int second,
        vector<vector<int> >& quadruplets)
    {
        int left = second + 1;
        int right = arr.size() - 1;
  
        while (left < right) {
            int sum
                = arr[first]
                  + arr[second]
                  + arr[left]
                  + arr[right];
  
            if (sum == targetSum) {
  
                // Found the quadruplet
                quadruplets
                    .push_back(
                        { arr[first], arr[second],
                          arr[left],
                          arr[right] });
                left++;
                right--;
  
                // Skip same element to avoid
                // duplicate quadruplets
                while (left < right
                       && arr[left]
                              == arr[left - 1]) {
                    left++;
                }
  
                // Skip same element to avoid
                // duplicate quadruplets
                while (left < right
                       && arr[right]
                              == arr[right + 1]) {
                    right--;
                }
            }
  
            // We need a pair
            // with a bigger sum
            else if (sum < targetSum) {
                left++;
            }
  
            // We need a pair
            // with a smaller sum
            else {
                right--;
            }
        }
    }
};
  
void printQuad(
    vector<int>& vec, int target)
{
  
    // Function call
    auto result
        = QuadrupleSumToTarget::
            searchQuadruplets(
                vec, target);
  
    // Print Quadruples
    for (int j = 0; j < result.size(); j++) {
        vector<int> vec = result[j];
        if (j == 0)
            cout << "[";
  
        for (int i = 0; i < vec.size(); i++) {
  
            if (i == 0)
                cout << "[";
            cout << vec[i];
            if (i != vec.size() - 1)
                cout << ", ";
            else
                cout << "]";
        }
  
        if (j != result.size() - 1)
            cout << ", ";
        else
            cout << "]";
    }
}
  
// Driver code
int main(int argc, char* argv[])
{
    vector<int> vec
        = { 4, 1, 2,
            -1, 1, -3 };
    int target = 1;
  
    printQuad(vec, target);
  
    return 0;
}

Output:

[[-3, -1, 1, 4], [-3, 1, 1, 2]]

Time complexity: Sorting the array will take O(N*logN). Overall searchQuadruplets() will take O(N * logN + N^3), which is asymptotically equivalent to O(N^3).

Auxiliary Space complexity: The auxiliary space complexity of the above algorithm will be O(N) which is required for sorting.

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