Four Sum Problem All Unique Quadruplets in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Four Sum problem?

The Four Sum problem asks to find all unique groups of four numbers in an array that add up to a given target sum.

beginner

Why do we sort the array before solving the Four Sum problem?

Sorting helps to efficiently skip duplicates and use two-pointer technique to find pairs that sum to a target, reducing complexity.

intermediate

Explain the two-pointer technique used in the Four Sum problem.

After fixing two numbers, two pointers start from the ends of the remaining array segment and move inward to find pairs that sum to the remaining target.

intermediate

How do we avoid duplicate quadruplets in the Four Sum solution?

We skip over numbers that are the same as the previous one at each step (for first, second, and during two-pointer search) to ensure uniqueness.

intermediate

What is the time complexity of the Four Sum problem solution using sorting and two pointers?

The time complexity is O(n^3) because we use two nested loops and a two-pointer scan inside them.

What is the first step in solving the Four Sum problem efficiently?

A Use a hash map

B Sort the array

C Reverse the array

D Remove duplicates first

Sorting the array helps to use two-pointer technique and skip duplicates easily.

In the Four Sum problem, after fixing two numbers, what technique is used to find the other two?

A Two-pointer technique

B Recursion

C Binary search

D Brute force

Two-pointer technique efficiently finds pairs that sum to the remaining target.

How do we ensure quadruplets are unique in the Four Sum problem?

A By sorting only

B By using a set to store quadruplets

C By sorting and skipping duplicates

D By using recursion

Sorting and skipping duplicates at each step prevents repeated quadruplets.

What is the overall time complexity of the Four Sum solution using sorting and two pointers?

A O(n^3)

B O(n log n)

C O(n^4)

D O(n^2)

Two nested loops and a two-pointer scan inside give O(n^3) complexity.

Which of these is NOT a step in the Four Sum solution?

A Sort the array

B Fix two numbers with loops

C Use two pointers to find pairs

D Use dynamic programming

Dynamic programming is not used in the standard Four Sum solution.

Describe the step-by-step approach to solve the Four Sum problem with unique quadruplets.

Think about how sorting and two pointers help find quadruplets without repeats.

Explain how skipping duplicates works in the Four Sum problem to avoid repeated quadruplets.

Duplicates appear next to each other after sorting.