Python Bisect: Find four elements from a given array of integers whose sum is equal to a given number

Last update on April 23 2025 12:49:00 (UTC/GMT +8 hours)

9. Quadruplet Sum Equals Target

Write a Python program to find four elements from a given array of integers whose sum is equal to a given number. The solution set must not contain duplicate quadruplets.

Sample Solution:

Python Code:

#Source: https://bit.ly/2SSoyhf
from bisect import bisect_left
class Solution:
    def fourSum(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: List[List[int]]
        """
        N = 4
        quadruplets = []
        if len(nums) < N:
            return quadruplets
        nums = sorted(nums)
        quadruplet = []

        # Let top[i] be the sum of largest i numbers.
        top = [0]       
        for i in range(1, N):
            top.append(top[i - 1] + nums[-i])

        # Find range of the least number in curr_n (0,...,N)
        # numbers that sum up to curr_target, then find range
        # of 2nd least number and so on by recursion.
        def sum_(curr_target, curr_n, lo=0):
            if curr_n == 0:
                if curr_target == 0:
                    quadruplets.append(quadruplet[:])
                return

            next_n = curr_n - 1
            max_i = len(nums) - curr_n
            max_i = bisect_left(
                nums, curr_target // curr_n,
                lo, max_i)
            min_i = bisect_left(
                nums, curr_target - top[next_n],
                lo, max_i)

            for i in range(min_i, max_i + 1): 
                if i == min_i or nums[i] != nums[i - 1]:
                    quadruplet.append(nums[i])
                    next_target = curr_target - nums[i]
                    sum_(next_target, next_n, i + 1)
                    quadruplet.pop()

        sum_(target, N)
        return quadruplets

s = Solution()
nums = [-2, -1, 1, 2, 3, 4, 5, 6]
target = 10
result = s.fourSum(nums, target)
print("\nArray values & target value:",nums,"&",target)
print("Solution Set:\n", result)

Sample Output:

Array values & target value: [-2, -1, 1, 2, 3, 4, 5, 6] & 10
Solution Set:
 [[-2, 1, 5, 6], [-2, 2, 4, 6], [-2, 3, 4, 5], [-1, 1, 4, 6], [-1, 2, 3, 6], [-1, 2, 4, 5], [1, 2, 3, 4]]

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to find all unique quadruplets in an array that sum up to a given target, using a combination of binary search and two-pointer techniques.
Write a Python script to implement a function that returns a list of quadruplets whose sum equals the target, ensuring that no duplicate quadruplets are included.
Write a Python program to search for four numbers in an array that add up to a specified target using bisect for optimizing inner loop searches.
Write a Python function to output all valid quadruplets from a sorted list that sum to a target value, taking care to skip duplicate values during iteration.

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