Introduction

In this blog post, we will explore how to solve the LeetCode problem "1943" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

There is a long and thin painting that can be represented by a number line. The painting was painted with multiple overlapping segments where each segment was painted with a unique color. You are given a 2D integer array segments, where segments[i] = [starti, endi, colori] represents the half-closed segment [starti, endi) with colori as the color. The colors in the overlapping segments of the painting were mixed when it was painted. When two or more colors mix, they form a new color that can be represented as a set of mixed colors. For example, if colors 2, 4, and 6 are mixed, then the resulting mixed color is {2,4,6}. For the sake of simplicity, you should only output the sum of the elements in the set rather than the full set. You want to describe the painting with the minimum number of non-overlapping half-closed segments of these mixed colors. These segments can be represented by the 2D array painting where painting[j] = [leftj, rightj, mixj] describes a half-closed segment [leftj, rightj) with the mixed color sum of mixj. For example, the painting created with segments = [[1,4,5],[1,7,7]] can be described by painting = [[1,4,12],[4,7,7]] because: [1,4) is colored {5,7} (with a sum of 12) from both the first and second segments. [4,7) is colored {7} from only the second segment. Return the 2D array painting describing the finished painting (excluding any parts that are not painted). You may return the segments in any order. A half-closed segment [a, b) is the section of the number line between points a and b including point a and not including point b. Example 1: Input: segments = [[1,4,5],[4,7,7],[1,7,9]] Output: [[1,4,14],[4,7,16]] Explanation: 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]] Explanation: 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]] Explanation: 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.

Explanation

Here's the breakdown of the approach, complexity, and the Python code:

• High-level approach:

  • Use a sweep line algorithm. Create a timeline of events (start and end points of segments).
  • Maintain a running sum of colors active at each point in the timeline.
  • When the running sum changes, record the segment and its color sum.

• Complexity:

  • Runtime Complexity: O(N log N), where N is the number of segments (due to sorting).
  • Storage Complexity: O(N)

Code

    def splitPainting(segments):
    """
    Calculates the minimum number of non-overlapping segments describing the painting.

    Args:
        segments: A list of segments, where each segment is a list [start, end, color].

    Returns:
        A list of segments, where each segment is a list [left, right, mix_sum].
    """

    events = {}
    for start, end, color in segments:
        if start not in events:
            events[start] = 0
        if end not in events:
            events[end] = 0
        events[start] += color
        events[end] -= color

    timeline = sorted(events.keys())
    result = []
    current_sum = 0

    for i in range(len(timeline) - 1):
        start = timeline[i]
        end = timeline[i + 1]
        current_sum += events[start]

        if current_sum > 0:
            result.append([start, end, current_sum])

    return result