How do you solve Describe the Painting on LeetCode?

Describe the Painting (LeetCode #1943) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Using a sweep line algorithm can significantly reduce the complexity of overlapping interval problems.

What is the time complexity of Describe the Painting?

The optimal solution for Describe the Painting runs in O(n log n) time and uses O(n) space. The sorting of events takes O(n log n), and maintaining the hashmap for active colors takes linear space.

What is the brute force solution for Describe the Painting?

The brute force approach for Describe the Painting is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking each segment against every other segment to determine the colors that overlap. This method is straightforward but inefficient, especially for larger inputs. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Describe the Painting?

Describe the Painting uses the following concepts: Array, Hash Table, Sorting, Prefix Sum. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Describe the Painting?

Always clarify the problem requirements and constraints before diving into coding. Think about edge cases, such as segments that do not overlap at all. Practice explaining your thought process as you code, as this is crucial in interviews.

What are common mistakes when solving Describe the Painting?

Failing to account for overlapping segments correctly. Not using data structures like HashMap or Set effectively to manage colors.

#1943

Describe the Painting

Medium

ArrayHash TableSortingPrefix SumHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

💡

Intuition

Time O(n log n)Space O(n)

The optimal solution uses a sweep line algorithm to efficiently track overlapping segments and their colors. By sorting the segments and using a map to keep track of color sums, we can achieve a more efficient solution.

⚙️

Algorithm

4 steps

1Step 1: Create an array of events for each segment's start and end points.
2Step 2: Sort the events by position, processing starts before ends at the same position.
3Step 3: Use a hashmap to track the sum of colors currently active as we sweep through the events.
4Step 4: When moving to a new position, if there are active colors, create a new segment with their sum.

solution.py27 lines

1# Full working Python code
2from collections import defaultdict
3
4def describe_painting(segments):
5    events = []
6    for start, end, color in segments:
7        events.append((start, color, 'start'))
8        events.append((end, color, 'end'))
9    events.sort()
10
11    color_sum = defaultdict(int)
12    painting = []
13    last_position = None
14
15    for position, color, typ in events:
16        if last_position is not None and last_position != position:
17            if color_sum:
18                painting.append([last_position, position, sum(color_sum.keys())])
19        if typ == 'start':
20            color_sum[color] += 1
21        else:
22            del color_sum[color]
23        last_position = position
24
25    return painting
26
27print(describe_painting([[1, 4, 5], [1, 7, 7]]))

ℹ

Complexity note: The sorting of events takes O(n log n), and maintaining the hashmap for active colors takes linear space.

1Using a sweep line algorithm can significantly reduce the complexity of overlapping interval problems.
2Tracking active colors dynamically allows for efficient summation without unnecessary recalculations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.