Is Design an Array Statistics Tracker easy or hard?

Design an Array Statistics Tracker is classified as a Hard problem because it requires coordinating multiple data structures and maintaining statistics dynamically. Efficient implementations must handle insertions, deletions, and queries while preserving sorted order and frequency information.

Design an Array Statistics Tracker Python/Java solution

Python implementations usually rely on collections like deque for the queue, dictionaries for frequency maps, and libraries such as SortedList to maintain ordered elements. Java implementations commonly use ArrayDeque, HashMap, and TreeMap or TreeSet to maintain sorted order and frequencies.

How to solve Design an Array Statistics Tracker in O(n)?

A simple O(n) style solution stores all elements and recomputes statistics whenever needed. Mean requires scanning the array, median requires sorting or selecting the middle element, and mode requires building a frequency map. This approach is easier to implement but inefficient for frequent updates.

Is Design an Array Statistics Tracker asked at Google/Amazon/Meta?

Problems that require designing dynamic statistic trackers appear frequently in system design and advanced data structure interviews at companies like Google, Amazon, and Meta. They test your ability to combine multiple data structures such as heaps, hash maps, and ordered sets efficiently.

What is the best approach for Design an Array Statistics Tracker ?

The most efficient solution uses a combination of a queue, hash table, and ordered set. The queue keeps track of insertion order, the hash table maintains element frequencies for mode calculation, and the ordered set maintains sorted order for median queries. This design supports updates in O(log n) time while keeping queries fast.

What data structure is used in Design an Array Statistics Tracker ?

The optimized solution typically uses a queue for insertion order, a hash table for frequency tracking, and an ordered set or balanced tree for maintaining sorted values. Together they allow efficient updates and quick access to statistical measures like median and mode.

What is the time complexity of Design an Array Statistics Tracker ?

Using the optimal design, each insertion or deletion takes O(log n) due to ordered set updates. Frequency updates in the hash table are O(1). Mean queries are O(1), while median or mode queries are typically O(1) or O(log n) depending on the implementation.

3369. Design an Array Statistics Tracker - Practice Online

Design a data structure that keeps track of the values in it and answers some queries regarding their mean, median, and mode.

Implement the StatisticsTracker class.

StatisticsTracker(): Initialize the StatisticsTracker object with an empty array.
void addNumber(int number): Add number to the data structure.
void removeFirstAddedNumber(): Remove the earliest added number from the data structure.
int getMean(): Return the floored mean of the numbers in the data structure.
int getMedian(): Return the median of the numbers in the data structure.
int getMode(): Return the mode of the numbers in the data structure. If there are multiple modes, return the smallest one.

Note:

The mean of an array is the sum of all the values divided by the number of values in the array.
The median of an array is the middle element of the array when it is sorted in non-decreasing order. If there are two choices for a median, the larger of the two values is taken.
The mode of an array is the element that appears most often in the array.

Example 1:

Input:
["StatisticsTracker", "addNumber", "addNumber", "addNumber", "addNumber", "getMean", "getMedian", "getMode", "removeFirstAddedNumber", "getMode"]
[[], [4], [4], [2], [3], [], [], [], [], []]

Output:
[null, null, null, null, null, 3, 4, 4, null, 2]

Explanation

StatisticsTracker statisticsTracker = new StatisticsTracker();
statisticsTracker.addNumber(4); // The data structure now contains [4]
statisticsTracker.addNumber(4); // The data structure now contains [4, 4]
statisticsTracker.addNumber(2); // The data structure now contains [4, 4, 2]
statisticsTracker.addNumber(3); // The data structure now contains [4, 4, 2, 3]
statisticsTracker.getMean(); // return 3
statisticsTracker.getMedian(); // return 4
statisticsTracker.getMode(); // return 4
statisticsTracker.removeFirstAddedNumber(); // The data structure now contains [4, 2, 3]
statisticsTracker.getMode(); // return 2

Example 2:

Input:
["StatisticsTracker", "addNumber", "addNumber", "getMean", "removeFirstAddedNumber", "addNumber", "addNumber", "removeFirstAddedNumber", "getMedian", "addNumber", "getMode"]
[[], [9], [5], [], [], [5], [6], [], [], [8], []]

Output:
[null, null, null, 7, null, null, null, null, 6, null, 5]

Explanation

StatisticsTracker statisticsTracker = new StatisticsTracker();
statisticsTracker.addNumber(9); // The data structure now contains [9]
statisticsTracker.addNumber(5); // The data structure now contains [9, 5]
statisticsTracker.getMean(); // return 7
statisticsTracker.removeFirstAddedNumber(); // The data structure now contains [5]
statisticsTracker.addNumber(5); // The data structure now contains [5, 5]
statisticsTracker.addNumber(6); // The data structure now contains [5, 5, 6]
statisticsTracker.removeFirstAddedNumber(); // The data structure now contains [5, 6]
statisticsTracker.getMedian(); // return 6
statisticsTracker.addNumber(8); // The data structure now contains [5, 6, 8]
statisticsTracker.getMode(); // return 5

Constraints:

1 <= number <= 10⁹
At most, 10⁵ calls will be made to addNumber, removeFirstAddedNumber, getMean, getMedian, and getMode in total.
removeFirstAddedNumber, getMean, getMedian, and getMode will be called only if there is at least one element in the data structure.