How to Solve Snapshot Array

To solve SnapshotArray, we maintain a versioned list for each index to efficiently record value changes with corresponding snap_ids. Using binary search on these lists allows O(log n) retrieval for get operations. This approach prevents scanning the entire array for historical values and ensures set, snap, and get operations scale efficiently under constraints.

Problem Statement

Design a SnapshotArray class that supports initializing with a given length and provides set, snap, and get methods. The set method updates an element at a specified index, snap captures a snapshot of the current state and returns a unique snap_id, and get retrieves the value at a given index for a specific snap_id.

Constraints include array length up to 5 * 10^4, element values up to 10^9, snap_id within the number of snapshots taken, and up to 5 * 10^4 calls across all methods. The challenge is to handle multiple snapshots efficiently without scanning the full array each time.

Examples

Example 1

Input: ["SnapshotArray","set","snap","set","get"] [[3],[0,5],[],[0,6],[0,0]]

Output: [null,null,0,null,5]

SnapshotArray snapshotArr = new SnapshotArray(3); // set the length to be 3 snapshotArr.set(0,5); // Set array[0] = 5 snapshotArr.snap(); // Take a snapshot, return snap_id = 0 snapshotArr.set(0,6); snapshotArr.get(0,0); // Get the value of array[0] with snap_id = 0, return 5

Constraints

• 1 <= length <= 5 * 104
• 0 <= index < length
• 0 <= val <= 109
• 0 <= snap_id < (the total number of times we call snap())
• At most 5 * 104 calls will be made to set, snap, and get.

Solution Approach

Use Versioned Lists for Each Index

Maintain a list of (snap_id, value) pairs for each array index. On set, append or update the latest pair; on snap, increment the snap counter. This allows constant-time updates and avoids full array copying.

Binary Search for Efficient Retrieval

For get(index, snap_id), perform a binary search on the versioned list at that index to find the largest snap_id less than or equal to the requested one. This ensures O(log n) lookup and aligns with the array scanning plus hash lookup pattern.

Optimize Memory by Storing Changes Only

Instead of storing the entire array for each snapshot, only store changes at each index. This reduces space complexity and prevents redundant data, crucial for scaling to tens of thousands of operations.

Complexity Analysis

Time complexity is O(n \log n + k), where n is the number of set operations and k is the number of get queries, due to binary search per get. Space complexity is O(n + k) because we only store modified elements per snap rather than full array copies.

What Interviewers Usually Probe

• Expectations that each index maintains its own change history to avoid O(n) scanning.
• Focus on using binary search to optimize get operations over historical snapshots.
• Discussion on trade-offs between memory usage and snapshot speed is important.

Common Pitfalls or Variants

Common pitfalls

• Storing full arrays on each snap causes memory overflow for large inputs.
• Using linear search in get leads to TLE for many operations.
• Forgetting to append initial value (e.g., 0) for all indices before the first snap can produce incorrect results.

Follow-up variants

• SnapshotArray with range updates instead of single index updates.
• Persistent segment tree approach to maintain snapshot history for large arrays.
• Tracking multiple attributes per index, requiring nested versioned lists.

How GhostInterview Helps

• Automatically generates index-level version tracking to streamline Snap and Get operations.
• Highlights binary search retrieval patterns to prevent naive array scanning errors.
• Identifies memory-efficient strategies by only storing changes per snap instead of full arrays.

Topic Pages

• Array
• Hash Table
• Binary Search
• Design

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FAQ

What is the primary pattern in SnapshotArray?

The problem uses an array scanning plus hash lookup pattern, where each index stores a history of changes for fast retrieval.

How does get work efficiently in SnapshotArray?

get uses binary search on the versioned list of the target index to locate the most recent value before or at the given snap_id.

Why not copy the whole array on each snap?

Copying the full array each time leads to O(n * snapshots) space, which is inefficient and unnecessary since only changed elements need tracking.

What are the constraints for the SnapshotArray problem?

Array length is up to 5 * 10^4, values up to 10^9, snap_id less than total snaps, and at most 5 * 10^4 calls for set, snap, and get combined.

Can this approach handle thousands of snaps efficiently?

Yes, storing only changes per index and using binary search ensures both time and space efficiency even for tens of thousands of operations.