Find Circular Gift Exchange Chains solution and explanation
The problem
Table: SecretSanta
+-------------+------+ | Column Name | Type | +-------------+------+ | giver_id | int | | receiver_id | int | | gift_value | int | +-------------+------+ (giver_id, receiver_id) is the unique key for this table. Each row represents a record of a gift exchange between two employees, giver_id represents the employee who gives a gift, receiver_id represents the employee who receives the gift and gift_value represents the value of the gift given.
Write a solution to find the total gift value and length of circular chains of Secret Santa gift exchanges:
A circular chain is defined as a series of exchanges where:
- Each employee gives a gift to exactly one other employee.
- Each employee receives a gift from exactly one other employee.
- The exchanges form a continuous loop (e.g., employee A gives a gift to B, B gives to C, and C gives back to A).
Return the result ordered by the chain length and total gift value of the chain in descending order. If multiple different chains have the same chain_length and total_gift_value, include that combination only once.
The result format is in the following example.
Example:
Input:
SecretSanta table:
+----------+-------------+------------+ | giver_id | receiver_id | gift_value | +----------+-------------+------------+ | 1 | 2 | 20 | | 2 | 3 | 30 | | 3 | 1 | 40 | | 4 | 5 | 25 | | 5 | 4 | 35 | +----------+-------------+------------+
Output:
+----------+--------------+------------------+ | chain_id | chain_length | total_gift_value | +----------+--------------+------------------+ | 1 | 3 | 90 | | 2 | 2 | 60 | +----------+--------------+------------------+
Explanation:
- Chain 1 involves employees 1, 2, and 3:
- Employee 1 gives a gift to 2, employee 2 gives a gift to 3, and employee 3 gives a gift to 1.
- Total gift value for this chain = 20 + 30 + 40 = 90.
- Chain 2 involves employees 4 and 5:
- Employee 4 gives a gift to 5, and employee 5 gives a gift to 4.
- Total gift value for this chain = 25 + 35 = 60.
The result table is ordered by the chain length and total gift value of the chain in descending order.
Approach overview
Problem Overview: Each person in a gift exchange gives to exactly one receiver. A circular chain is a sequence of people where the gifts loop back to the starting person. You need to identify these loops and report them.
Approach 1: Brute Force Chain Walk (O(n^2) time, O(n) space)
Start from every person and follow the giver-to-receiver links one step at a time. Stop when you return to the starting person (a circle found) or revisit a node that is not the start (no circle from here). This works because each person has only one outgoing link, so the path from any starting point is fully determined. The cost comes from re-walking the same chains from every starting node, which can repeat work across n starts.
Approach 2: Hash Map with Memoized Path Results (O(n) time, O(n) space)
Store each person's receiver in a hash map so each link lookup is O(1). Keep a memo that records whether a node is already known to lead into a cycle or to a dead end. When a walk reaches a memoized node, you stop immediately and reuse the stored answer. Every node gets resolved once, so total work is linear. Prefer this when the input is given as a list of pairs and you want a simple, readable solution.
Approach 3: Visited-State Traversal with Three Colors (O(n) time, O(n) space)
Mark each node as unvisited, in the current path, or finished. Walk forward along the chain. If you hit a node marked as in the current path, you found a cycle, and the cycle consists of the nodes from that point onward in your path. If you hit a finished node, the path above it cannot form a new cycle. This approach extracts the exact members of each circle, not just their existence, and it uses no recursion, so it avoids stack depth issues on long chains.
Recommended for interviews: Interviewers expect the linear approach. The brute force shows you understand what a circular chain is and can trace it correctly. The O(n) solution with visited states shows you can avoid redundant traversal and reason about the structure of a graph where every node has one outgoing edge. Explain why each node is processed once before you code.
Related topics: graph, hash table, depth-first search.
The written solution for this problem is still being prepared. Try it yourself in the meantime.
Try solving it yourselfComplexity analysis
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Brute Force Chain Walk | O(n^2) | O(n) | Small inputs or first pass to confirm logic |
| Hash Map with Memoization | O(n) | O(n) | General case, need count or existence of cycles |
| Visited-State Traversal | O(n) | O(n) | When you must list the members of each circle |
Frequently asked questions
Find Circular Gift Exchange Chains Python solution?
Build a dictionary mapping each giver to their receiver, then iterate over all people. For each unvisited person, follow the receiver links while recording the path in a set or list with states. Return the cycles found when a node reappears within the current path. The solution runs in O(n) time and O(n) space.
Is Find Circular Gift Exchange Chains easy or hard?
It is rated Hard on FleetCode with a 50.7 percent acceptance rate. The difficulty comes from correctly handling chains that lead into a cycle without being part of it, not from the coding itself. Mastering the three-state traversal makes it manageable.
How to solve Find Circular Gift Exchange Chains in O(n)?
Store each giver's receiver in a hash map, then walk each unvisited chain while marking nodes as in-progress or finished. When a walk hits an in-progress node, a cycle exists and consists of the nodes from that point in the current path. When it hits a finished node, stop, because that path cannot close a new cycle.
What is the best approach for Find Circular Gift Exchange Chains?
The best approach is a linear traversal that processes each person once, using a hash map for receiver lookups and visited states to detect loops. It runs in O(n) time with O(n) extra space. The brute force walk from every node is correct but runs in O(n^2).
What data structure is used in Find Circular Gift Exchange Chains?
A hash map stores each person's receiver for constant-time lookup. A visited or state array tracks whether each node is unvisited, in the current path, or finished. The structure is effectively a directed graph where every node has one outgoing edge.
What is the time complexity of Find Circular Gift Exchange Chains?
The optimal solution runs in O(n) time, where n is the number of people in the exchange. Each person is visited a constant number of times across all walks. The naive approach that restarts a walk from every person runs in O(n^2).
Is Find Circular Gift Exchange Chains asked at Google, Amazon, or Meta?
The problem is tagged General on FleetCode, so no company-specific frequency is listed for it. Graph traversal and cycle detection questions like this appear often in interview loops at large tech companies. Check recent interview reports for current company-specific data.