#1943

Medium

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Describe the Painting

Solve the problem of describing a painted segment with mixed colors using array scanning and hash table lookups.

Problem Statement

You are given a long and thin painting represented by a number line. The painting has multiple overlapping segments where each segment is painted with a unique color. Each segment is represented by a 3-element array [start, end, color] where 'start' is the start point, 'end' is the endpoint, and 'color' is the color of the segment. Your goal is to return the sum of colors over each of the segments.

Overlapping segments mix their colors. When multiple segments overlap, you must calculate the sum of the colors over each non-overlapping part. The result should reflect the sum of all unique colors in the overlapping region without listing individual colors, just their summed values.

Examples

Example 1

Input: segments = [[1,4,5],[4,7,7],[1,7,9]]

Output: [[1,4,14],[4,7,16]]

The painting can be described as follows:

[1,4) is colored {5,9} (with a sum of 14) from the first and third segments.
[4,7) is colored {7,9} (with a sum of 16) from the second and third segments.

Example 2

Input: segments = [[1,7,9],[6,8,15],[8,10,7]]

Output: [[1,6,9],[6,7,24],[7,8,15],[8,10,7]]

The painting can be described as follows:

[1,6) is colored 9 from the first segment.
[6,7) is colored {9,15} (with a sum of 24) from the first and second segments.
[7,8) is colored 15 from the second segment.
[8,10) is colored 7 from the third segment.

Example 3

Input: segments = [[1,4,5],[1,4,7],[4,7,1],[4,7,11]]

Output: [[1,4,12],[4,7,12]]

The painting can be described as follows:

[1,4) is colored {5,7} (with a sum of 12) from the first and second segments.
[4,7) is colored {1,11} (with a sum of 12) from the third and fourth segments. Note that returning a single segment [1,7) is incorrect because the mixed color sets are different.

Constraints

1 <= segments.length <= 2 * 104
segments[i].length == 3
1 <= starti < endi <= 105
1 <= colori <= 109
Each colori is distinct.

Solution Approach

Sorting the segments

Sort the segments based on their starting point. This allows us to efficiently handle overlaps and calculate the sum of colors for each distinct range by scanning through the sorted segments.

Array scanning and Hash table for sum

Use a hash table to store the colors for each segment. As we scan through the segments, we update the color sums and adjust for any overlaps by merging adjacent ranges.

Merging overlapping ranges

Once sorted, iterate through the segments, merging them where they overlap. For each merged range, compute the sum of the unique colors in that range and add it to the result.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity is O(N log N) due to the sorting of segments, where N is the number of segments. The space complexity is O(N) because we store color sums and ranges in the hash table during the scanning process.

What Interviewers Usually Probe

Can the candidate identify that sorting the segments first simplifies the merging of overlaps?
Is the candidate able to efficiently use a hash table for color summation during the scan?
Does the candidate handle edge cases like non-overlapping or fully contained segments?

Common Pitfalls or Variants

Common pitfalls

Failing to correctly handle overlapping ranges and their color sums.
Not sorting the segments, which would lead to inefficiencies in handling overlaps.
Misunderstanding the requirement to only sum the colors in the overlapping regions and not return the full list of colors.

Follow-up variants

Handling segments with large color ranges or many overlaps efficiently.
Optimizing for time and space when the number of segments grows large.
Modifying the problem to return the full list of colors for each segment instead of just the sum.

FAQ

What is the main approach for solving the 'Describe the Painting' problem?

The main approach is sorting the segments and then scanning through them while using a hash table to handle color sums in overlapping regions.

How do overlapping segments affect the solution?

Overlapping segments require merging ranges and summing the colors, which can be handled efficiently by sorting the segments first.

Can I use a different data structure instead of a hash table for summing colors?

While hash tables are efficient for this task, other data structures like arrays or trees might also work, but they may not be as optimal for this particular problem.

What are the time and space complexities for this problem?

The time complexity is O(N log N) due to sorting, and the space complexity is O(N) for storing the color sums and ranges.

What is the significance of sorting the segments in the 'Describe the Painting' problem?

Sorting the segments allows you to efficiently merge overlapping ranges and calculate the sum of the colors in each distinct range without unnecessary recomputation.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def splitPainting(self, segments: List[List[int]]) -> List[List[int]]:
        d = defaultdict(int)
        for l, r, c in segments:
            d[l] += c
            d[r] -= c
        s = sorted([[k, v] for k, v in d.items()])
        n = len(s)
        for i in range(1, n):
            s[i][1] += s[i - 1][1]
        return [[s[i][0], s[i + 1][0], s[i][1]] for i in range(n - 1) if s[i][1]]

Continue Practicing

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