Adjacency list pattern in DynamoDB - Time & Space Complexity

Time Complexity: Adjacency list pattern

O(n)

Understanding Time Complexity

When working with the adjacency list pattern in DynamoDB, it's important to understand how the time to get connected items grows as the list grows.

We want to know how the number of operations changes when we fetch related nodes.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Fetch all child nodes for a given parent node
const params = {
  TableName: "GraphTable",
  KeyConditionExpression: "ParentId = :pid",
  ExpressionAttributeValues: {
    ":pid": { S: "parent123" }
  }
};
const result = await dynamodb.query(params).promise();
return result.Items;
    

This code fetches all child nodes linked to a specific parent node using the adjacency list pattern.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Querying DynamoDB to get all children of one parent.
• How many times: Once per parent node, but returns multiple child items.

How Execution Grows With Input

As the number of children for a parent grows, the query returns more items, so the work grows with the number of children.

Input Size (n = number of children)	Approx. Operations
10	About 10 items fetched
100	About 100 items fetched
1000	About 1000 items fetched

Pattern observation: The time grows roughly in direct proportion to the number of children returned.

Final Time Complexity

Time Complexity: O(n)

This means the time to get all children grows linearly with how many children there are.

Common Mistake

[X] Wrong: "Querying a parent node always takes constant time regardless of children count."

[OK] Correct: The query returns all children, so if there are many children, it takes longer to fetch and process them all.

Interview Connect

Understanding how data retrieval time grows with connected items helps you design efficient queries and explain your choices clearly in interviews.

Self-Check

"What if we added pagination to limit the number of children returned per query? How would the time complexity change?"

Practice

1. What does the adjacency list pattern store in each item to represent relationships in DynamoDB?

easy

A. The parent item's identifier

B. The list of all child items

C. The full path from root to the item

D. The depth level of the item in the hierarchy

Solution

1. Step 1: Understand adjacency list pattern basics

   The adjacency list pattern stores a reference to the parent item for each node to represent hierarchy.

2. Step 2: Identify what is stored per item

   Each item contains the parent's ID, not the children or full path or depth.

3. Final Answer:

   The parent item's identifier -> Option A

4. Quick Check:

   Adjacency list = parent ID stored [OK]

Hint: Remember: adjacency list stores parent ID only [OK]

Common Mistakes:

• Thinking it stores all children in each item
• Confusing with storing full path or depth
• Assuming it stores unrelated metadata

2. Which of the following is the correct way to represent a parent-child relationship in a DynamoDB item using the adjacency list pattern?

easy

A. { "ItemId": "123", "Children": ["456", "789"] }

B. { "ItemId": "123", "ParentId": "456" }

C. { "ItemId": "123", "Path": "/root/456/123" }

D. { "ItemId": "123", "Depth": 2 }

Solution

1. Step 1: Identify adjacency list item structure

   Adjacency list stores the parent ID inside each item to link it to its parent.

2. Step 2: Match correct JSON structure

   { "ItemId": "123", "ParentId": "456" } shows an item with its own ID and a ParentId field, which is correct.

3. Final Answer:

   { "ItemId": "123", "ParentId": "456" } -> Option B

4. Quick Check:

   ParentId field present = adjacency list format [OK]

Hint: Look for ParentId key in item JSON [OK]

Common Mistakes:

• Using Children array instead of ParentId
• Including full path or depth instead of parent reference
• Confusing item ID with parent ID

3. Given the following DynamoDB items using adjacency list pattern:

{ "ItemId": "1", "ParentId": null }

{ "ItemId": "2", "ParentId": "1" }

{ "ItemId": "3", "ParentId": "1" }

{ "ItemId": "4", "ParentId": "2" }

If you query for items with ParentId = '1', which items will you get?

medium

A. [{ "ItemId": "2", "ParentId": "1" }, { "ItemId": "3", "ParentId": "1" }]

B. [{ "ItemId": "1", "ParentId": null }]

C. [{ "ItemId": "4", "ParentId": "2" }]

D. [{ "ItemId": "2", "ParentId": "1" }, { "ItemId": "3", "ParentId": "1" }, { "ItemId": "4", "ParentId": "2" }]

Solution

1. Step 1: Understand query condition

   The query filters items where ParentId equals '1'.

2. Step 2: Identify matching items

   Items with ParentId '1' are ItemId '2' and '3'. Item '4' has ParentId '2', so it does not match.

3. Final Answer:

   [{ "ItemId": "2", "ParentId": "1" }, { "ItemId": "3", "ParentId": "1" }] -> Option A

4. Quick Check:

   Filter ParentId='1' returns items 2 and 3 [OK]

Hint: Filter by ParentId to get direct children only [OK]

Common Mistakes:

• Including items with different ParentId values
• Confusing root item with children
• Assuming query returns grandchildren

4. You wrote this DynamoDB query to get children of item '5':

FilterExpression: "ParentId = :pid", ExpressionAttributeValues: { ":pid": "5" }

But it returns no results, even though you know children exist. What is the likely error?

medium

A. The ExpressionAttributeValues syntax is incorrect

B. You should use KeyConditionExpression instead of FilterExpression

C. You need to query with ItemId = '5' instead

D. ParentId attribute is missing or named differently in items

Solution

1. Step 1: Check attribute naming

   If ParentId attribute is missing or named differently, filter finds no matches.

2. Step 2: Verify attribute presence in items

   Ensure all child items have ParentId attribute exactly named 'ParentId'. If not, query returns empty.

3. Final Answer:

   ParentId attribute is missing or named differently in items -> Option D

4. Quick Check:

   Attribute name mismatch causes no results [OK]

Hint: Check attribute names match exactly in query and items [OK]

Common Mistakes:

• Confusing FilterExpression with KeyConditionExpression
• Incorrect syntax in ExpressionAttributeValues
• Querying by ItemId instead of ParentId

5. You want to retrieve the full hierarchy path from a child item up to the root using the adjacency list pattern in DynamoDB. Which approach is best?

hard

A. Use a DynamoDB join operation to combine parent and child items

B. Store the full path string in each item and query it directly

C. Iteratively query each item's ParentId until reaching the root

D. Use a single query filtering all items with ParentId equal to the child's ID

Solution

1. Step 1: Understand adjacency list limitations

   Adjacency list stores only parent references, so full path is not stored.

2. Step 2: Retrieve full path by iterative queries

   To get full path, query each item's parent repeatedly until root (ParentId null) is reached.

3. Step 3: Evaluate other options

   Store the full path string in each item and query it directly is a different pattern (materialized path). Use a single query filtering all items with ParentId equal to the child's ID gets children, not parents. Use a DynamoDB join operation to combine parent and child items is invalid as DynamoDB has no join.

4. Final Answer:

   Iteratively query each item's ParentId until reaching the root -> Option C

5. Quick Check:

   Adjacency list needs iterative parent queries for full path [OK]

Hint: Follow parent links step-by-step to build full path [OK]

Common Mistakes:

• Expecting DynamoDB to support joins
• Assuming full path is stored in adjacency list
• Trying to get full path with single query filtering children