3160. Find the Number of Distinct Colors Among the Balls - Detailed Explanation
Problem Statement
You are given an array (or list) of items representing the colors of balls. Each element in the array denotes the color of one ball (for example, using strings like "red", "blue", etc., or characters such as 'R', 'G', 'B'). You need to count and return the number of distinct colors present in the array.
Example Inputs and Explanations
-
Example 1:
- Input:
["red", "blue", "red", "green"] - Output:
3 - Explanation: The distinct colors are
"red","blue", and"green".
- Input:
-
Example 2:
- Input:
["yellow", "yellow", "yellow"] - Output:
1 - Explanation: All balls are yellow, so there is only 1 unique color.
- Input:
-
Example 3:
- Input:
["black", "white", "gray", "black", "white", "brown"] - Output:
4 - Explanation: The unique colors are
"black","white","gray", and"brown".
- Input:
Constraints
- The number of balls (i.e. the size of the array) can be large (for example, up to 10⁵).
- Each ball’s color is represented by a valid identifier (e.g., a string or a character).
- It is assumed that the input is non-empty (but you should always consider how to handle an empty input if that case arises).
Hints
- Hint 1: Think about how you might quickly determine if you have already seen a particular color. What data structure naturally helps with checking membership quickly?
- Hint 2: Consider how you might use the idea of “uniqueness.” A set data structure automatically stores only unique items.
- Hint 3: Alternatively, sorting the array and counting transitions between different elements is another way to count distinct items.
Approach 1: Using a HashSet (or Set in Python)
Idea
The most straightforward way to solve this problem is to use a hash set. As you iterate through the list of ball colors, you add each color to the set. Since sets do not store duplicates, the final size of the set gives the number of distinct colors.
Step-by-Step Walkthrough (Visual Example)
For the input:
["R", "R", "G", "B", "B", "G", "R"]
- Initialize an empty set.
- Iteration:
- Process the first ball: add
"R"→ set becomes{ "R" }. - Process the second ball:
"R"is already in the set. - Process the third ball: add
"G"→ set becomes{ "R", "G" }. - Process the fourth ball: add
"B"→ set becomes{ "R", "G", "B" }. - Process the next balls:
"B","G", and"R"are already in the set.
- Process the first ball: add
- Result:
The size of the set is 3, meaning there are 3 distinct colors.
Python Code
Java Code
Approach 2: Sorting and Counting Transitions
Idea
Another way to solve the problem is by first sorting the array. Once the array is sorted, identical colors will be adjacent to each other. Then, you can iterate through the sorted list and count the number of times a new color appears.
Step-by-Step Walkthrough
For the input:
["red", "blue", "red", "green"]
- Sort the array:
Sorted array might be["blue", "green", "red", "red"]. - Iteration:
- Start with the first color
"blue"and set the count to 1. - Move to
"green", which is different from"blue", increment the count to 2. - Move to
"red", which is different from"green", increment the count to 3. - The next
"red"is the same as the previous, so no change.
- Start with the first color
- Result:
The count is 3.
Discussion
- Pros:
– This approach is simple once the list is sorted. - Cons:
– Sorting takes O(n log n) time, which is less efficient than the O(n) set-based approach for very large inputs.
Complexity Analysis
-
Approach 1 (HashSet):
- Time Complexity: O(n), where n is the number of balls (each insertion is O(1) on average).
- Space Complexity: O(n) in the worst case (if all colors are distinct).
-
Approach 2 (Sorting):
- Time Complexity: O(n log n) due to sorting.
- Space Complexity: Depends on the sorting algorithm; typically O(1) if sorting in place or O(n) if additional space is used.
Common Mistakes and Edge Cases
Common Mistakes
-
Overcomplicating the Problem:
Since the task is to count distinct elements, trying to use overly complex data structures or algorithms (like maintaining frequency maps when a set is enough) can lead to unnecessary complications. -
Ignoring Case Sensitivity:
Ensure that if the colors are given as strings, you handle case sensitivity according to the problem’s requirements (e.g.,"Red"vs."red"). -
Not Preserving Input Integrity:
Sorting the array (if not done on a copy) might change the original order. If preserving order is required for other reasons, be careful with in-place operations.
Edge Cases
-
Empty Input Array:
Return 0 if the input array is empty. -
Single-Element Array:
Should correctly return 1. -
All Balls Same Color:
Should return 1, regardless of the number of balls.
Variations
-
Counting Distinct Elements in a Subarray:
Given a subarray (or multiple queries on subarrays), count the distinct elements. -
Finding the Most Frequent Color:
Instead of counting unique colors, determine which color appears most frequently.
Related Problems for Further Practice
-
Longest Substring Without Repeating Characters:
Involves tracking distinct characters in a substring. -
Top K Frequent Elements:
Requires counting frequencies and then selecting the most frequent elements. -
Count Unique Elements in an Array:
A fundamental problem that uses similar techniques.
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