Start by sorting the points by day to ensure sequential connection. Then check the slope between consecutive points to group collinear segments. Count each distinct line segment where slopes change, which gives the minimum number of lines required to represent the entire chart accurately.
Problem Statement
You are given a 2D array stockPrices where stockPrices[i] = [dayi, pricei] represents the stock price on day dayi. The points are plotted on an XY plane with dayi as X and pricei as Y, and adjacent points are connected to form a line chart. Your task is to compute the minimum number of straight lines needed to represent the line chart without altering the order of days.
Return an integer representing the minimum number of lines required. For example, given stockPrices = [[1,7],[2,6],[3,5],[4,4],[5,4],[6,3],[7,2],[8,1]], the correct output is 3 because three line segments suffice to connect all points with correct slopes.
Examples
Example 1
Input: stockPrices = [[1,7],[2,6],[3,5],[4,4],[5,4],[6,3],[7,2],[8,1]]
Output: 3
The diagram above represents the input, with the X-axis representing the day and Y-axis representing the price. The following 3 lines can be drawn to represent the line chart:
- Line 1 (in red) from (1,7) to (4,4) passing through (1,7), (2,6), (3,5), and (4,4).
- Line 2 (in blue) from (4,4) to (5,4).
- Line 3 (in green) from (5,4) to (8,1) passing through (5,4), (6,3), (7,2), and (8,1). It can be shown that it is not possible to represent the line chart using less than 3 lines.
Example 2
Input: stockPrices = [[3,4],[1,2],[7,8],[2,3]]
Output: 1
As shown in the diagram above, the line chart can be represented with a single line.
Constraints
- 1 <= stockPrices.length <= 105
- stockPrices[i].length == 2
- 1 <= dayi, pricei <= 109
- All dayi are distinct.
Solution Approach
Sort points by day
Arrange stockPrices in increasing order of dayi to ensure the chart progresses sequentially. This step is crucial because collinearity checks require consecutive points in time.
Check slopes between consecutive points
Compute the slope between each pair of consecutive points. Whenever the slope changes, it indicates a new line segment. This allows grouping of points that lie on the same straight line efficiently.
Count distinct line segments
Iterate through all points, tracking slope changes. Increment the line count each time a slope change occurs. The final count is the minimum number of lines needed to represent the chart.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is dominated by sorting, O(n log n), and slope checks take O(n), giving overall O(n log n). Space complexity is O(1) extra if in-place sorting is used.
What Interviewers Usually Probe
- Ask why sorting by day is necessary before checking slopes.
- Expect candidate to explain slope comparison without floating-point precision errors.
- Look for handling of edge cases where multiple points are collinear or duplicate prices exist.
Common Pitfalls or Variants
Common pitfalls
- Not sorting points by day before checking slopes, leading to incorrect line counts.
- Using floating-point division for slopes without reducing fractions, causing precision errors.
- Failing to handle cases where consecutive points have the same price or day order is not guaranteed.
Follow-up variants
- Calculate minimum lines if some points can be skipped or ignored to reduce total lines.
- Determine the number of lines needed for a 3D line chart instead of 2D.
- Optimize for streaming input where points arrive one by one and minimum lines must be updated online.
How GhostInterview Helps
- Automatically tracks slope changes to count line segments accurately in array plus math problems.
- Highlights edge cases where consecutive points appear collinear but require careful fraction comparison.
- Provides visual feedback and explanations for why certain points start a new line segment.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the main idea behind the Minimum Lines to Represent a Line Chart problem?
The key is to detect collinear points by checking slopes between consecutive points after sorting by day and counting each slope change as a new line.
Can we use floating-point slopes safely in this problem?
No, using floating-point slopes can cause precision errors; it is safer to compare slopes using cross multiplication of differences.
How does sorting affect the solution?
Sorting by day ensures that consecutive points are checked in chronological order, which is required for correct collinearity grouping.
What is the expected time complexity for this solution?
Sorting takes O(n log n) and slope checks take O(n), so the overall time complexity is O(n log n).
Is this problem only about arrays and math?
Yes, it primarily involves array manipulation to order points and math to calculate slopes, fitting the Array plus Math pattern.
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