Number of Distinct Values in O(n log n) Time Complexity using JavaScript

Given an array of integers, count how many distinct values exist in the array.

Example:

Input: [1, 5, -3, 1, -4, 2, -4, 7, 7]
Output: 6
Explanation: the distinct values in the array are [1, 5, -3, -4, 2, 7]

Note:

For this lesson, your algorithm should run in O(n log n) time and use O(1) extra space.
(There are faster solutions which we will discuss in future lessons)

Hints:

Let's sort the array in non-decreasing order. In this way all the equal elements will come one after another.

Then, we can traverse the sorted array from left to right using an index i. We should increment the solution if value nums[i] has not been seen before. How can we check this?

nums[i] has never been seen before if nums[i] != nums[i - 1].

Problem Definition

The task is to count the number of distinct values in a given array of integers.

Input: An array of integers.

Output: An integer representing the number of distinct values in the array.

Constraints:

The array can contain both positive and negative integers.
The array can have duplicate values.

Example:

Input: [1, 5, -3, 1, -4, 2, -4, 7, 7]
Output: 6
Explanation: The distinct values in the array are [1, 5, -3, -4, 2, 7]

Understanding the Problem

The core challenge is to identify and count unique values in the array. This problem is significant in various applications such as data analysis, where understanding the diversity of data points is crucial. A common pitfall is to use a naive approach that may not meet the time complexity requirements.

Approach

To solve this problem efficiently, we can use the following approach:

Sort the array in non-decreasing order. This ensures that all equal elements are adjacent.
Traverse the sorted array and count the number of unique elements by comparing each element with the previous one.

Let's discuss a naive solution and its limitations:

Naive Solution: Use a nested loop to compare each element with every other element to check for uniqueness. This approach has a time complexity of O(n^2), which is not efficient for large arrays.

Optimized Solution: By sorting the array first, we can reduce the problem to a linear scan, achieving a time complexity of O(n log n) due to the sorting step.

Algorithm

Here is a step-by-step breakdown of the optimized algorithm:

Sort the array in non-decreasing order.
Initialize a counter to keep track of distinct values.
Traverse the sorted array from the second element to the end.
For each element, compare it with the previous element. If they are different, increment the counter.
Return the counter value.

Code Implementation

// Function to count distinct values in an array
function countDistinctValues(arr) {
  // Step 1: Sort the array
  arr.sort((a, b) => a - b);

  // Step 2: Initialize the counter for distinct values
  let distinctCount = 1; // Start with 1 because the first element is always distinct

  // Step 3: Traverse the sorted array
  for (let i = 1; i < arr.length; i++) {
    // Step 4: Compare current element with the previous one
    if (arr[i] !== arr[i - 1]) {
      distinctCount++; // Increment counter if current element is different
    }
  }

  // Step 5: Return the count of distinct values
  return distinctCount;
}

// Example usage
const inputArray = [1, 5, -3, 1, -4, 2, -4, 7, 7];
console.log(countDistinctValues(inputArray)); // Output: 6

Complexity Analysis

Time Complexity: The sorting step takes O(n log n) time, and the traversal step takes O(n) time. Therefore, the overall time complexity is O(n log n).

Space Complexity: The algorithm uses O(1) extra space, as we are sorting the array in place and using a constant amount of additional space for the counter.

Edge Cases

Consider the following edge cases:

An empty array: The output should be 0.
An array with all identical elements: The output should be 1.
An array with all distinct elements: The output should be equal to the length of the array.

Examples:

Input: []
Output: 0

Input: [2, 2, 2, 2]
Output: 1

Input: [1, 2, 3, 4, 5]
Output: 5

Testing

To test the solution comprehensively, consider a variety of test cases, including simple, complex, and edge cases. You can use testing frameworks like Jest or Mocha for automated testing.

// Example test cases
console.log(countDistinctValues([])); // Output: 0
console.log(countDistinctValues([2, 2, 2, 2])); // Output: 1
console.log(countDistinctValues([1, 2, 3, 4, 5])); // Output: 5
console.log(countDistinctValues([1, 5, -3, 1, -4, 2, -4, 7, 7])); // Output: 6

Thinking and Problem-Solving Tips

When approaching such problems, consider the following tips:

Understand the problem requirements and constraints thoroughly.
Think about different approaches and their time and space complexities.
Start with a naive solution and then optimize it step by step.
Practice solving similar problems to improve your problem-solving skills.

Conclusion

In this blog post, we discussed how to count the number of distinct values in an array using an efficient algorithm with O(n log n) time complexity. We covered the problem definition, approach, algorithm, code implementation, complexity analysis, edge cases, and testing. Understanding and solving such problems is crucial for improving your algorithmic thinking and coding skills.

Additional Resources

For further reading and practice, consider the following resources:

LeetCode - Practice coding problems and challenges.
GeeksforGeeks - Tutorials and articles on algorithms and data structures.
MDN Web Docs - JavaScript documentation and tutorials.