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2280. Minimum Lines to Represent a Line Chart

Difficulty Topics

Description

You are given a 2D integer array stockPrices where stockPrices[i] = [dayi, pricei] indicates the price of the stock on day dayi is pricei. A line chart is created from the array by plotting the points on an XY plane with the X-axis representing the day and the Y-axis representing the price and connecting adjacent points. One such example is shown below:

Return the minimum number of lines needed to represent the line chart.

 

Example 1:

Input: stockPrices = [[1,7],[2,6],[3,5],[4,4],[5,4],[6,3],[7,2],[8,1]]
Output: 3
Explanation:
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
Explanation:
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

minimum-lines-to-represent-a-line-chart.py
class Solution:
    def minimumLines(self, stock: List[List[int]]) -> int:
        n = len(stock)

        if n == 1: return 0

        stock.sort(key = lambda x: x[0])
        dx = stock[0][0] - stock[1][0]
        dy = stock[0][1] - stock[1][1]

        res = 1

        for index in range(2, n):
            x, y = stock[index]

            dx1 = stock[index - 1][0] - stock[index][0]
            dy1 = stock[index - 1][1] - stock[index][1]  

            if dx1 * dy != dx * dy1:
                res += 1
                dx = dx1
                dy = dy1

        return res