How do you solve Minimum Lines to Represent a Line Chart on LeetCode?

Minimum Lines to Represent a Line Chart (LeetCode #2280) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding the concept of slopes helps in determining collinearity.

What is the time complexity of Minimum Lines to Represent a Line Chart?

The optimal solution for Minimum Lines to Represent a Line Chart runs in O(n) time and uses O(1) space. The complexity is O(n) because we only iterate through the sorted list once, making it linear in terms of the number of points.

What is the brute force solution for Minimum Lines to Represent a Line Chart?

The brute force approach for Minimum Lines to Represent a Line Chart is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach checks every triplet of consecutive points to see if they lie on the same line. If they do, we can skip counting a line segment for those points. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Lines to Represent a Line Chart?

Minimum Lines to Represent a Line Chart uses the following concepts: Array, Math, Geometry, Sorting, Number Theory. The recommended patterns to study are: Sorting, Geometry.

What are the interview tips for Minimum Lines to Represent a Line Chart?

Always clarify the problem requirements and constraints before jumping into coding. Discuss your thought process and approach with the interviewer; they may provide hints or guidance. Practice explaining your code as you write it; this helps solidify your understanding and prepares you for real interviews.

What are common mistakes when solving Minimum Lines to Represent a Line Chart?

Not sorting the points before processing, leading to incorrect slope calculations. Confusing the slope calculation leading to incorrect line counts.

#2280

Minimum Lines to Represent a Line Chart

Medium

ArrayMathGeometrySortingNumber TheorySortingGeometry

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

The optimal approach leverages the concept of slopes to determine when three consecutive points are collinear, allowing us to count lines more efficiently.

⚙️

Algorithm

5 steps

1Step 1: Sort the stockPrices array based on the day.
2Step 2: Initialize a counter for the number of lines needed.
3Step 3: Iterate through the sorted points and calculate the slope between the first two points.
4Step 4: For each subsequent point, check if the slope remains the same; if not, increment the line counter.
5Step 5: Return the total number of lines counted.

solution.py12 lines

1def minimumLines(stockPrices):
2    stockPrices.sort()
3    if len(stockPrices) < 2:
4        return 0
5    lines = 0
6    for i in range(1, len(stockPrices) - 1):
7        x1, y1 = stockPrices[i - 1]
8        x2, y2 = stockPrices[i]
9        x3, y3 = stockPrices[i + 1]
10        if (y2 - y1) * (x3 - x2) != (y3 - y2) * (x2 - x1):
11            lines += 1
12    return lines + 1

ℹ

Complexity note: The complexity is O(n) because we only iterate through the sorted list once, making it linear in terms of the number of points.

1Understanding the concept of slopes helps in determining collinearity.
2Sorting the points based on the x-axis (days) is crucial for correct slope calculations.

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