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Check If It Is a Straight Line

Difficulty: Easy

Problem Description

You are given an array coordinates, coordinates[i] = [x, y], where [x, y] represents the coordinate of a point. Check if these points make a straight line in the XY plane.

Key Insights

  • To determine if all points lie on a straight line, we can use the concept of the slope between consecutive points.
  • If the slope between any two segments formed by three points is the same, then the points are collinear.
  • The slope can be calculated using the formula (y2 - y1) / (x2 - x1). To avoid division and handle vertical lines, we can use cross multiplication.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we will:

  1. Use the first two points to establish a reference slope.
  2. Iterate through the remaining points and check if they maintain the same slope with the first point using cross multiplication to avoid division.
  3. If all points conform to the same slope, return true; otherwise, return false.

Code Solutions

def checkStraightLine(coordinates):
    if len(coordinates) < 2:
        return False

    # Get the differences for the first two points
    x0, y0 = coordinates[0]
    x1, y1 = coordinates[1]
    
    # Calculate the slope differences
    dx = x1 - x0
    dy = y1 - y0

    # Check each subsequent point
    for i in range(2, len(coordinates)):
        x, y = coordinates[i]
        # Cross multiplication to check slope equality
        if (y - y0) * dx != (x - x0) * dy:
            return False

    return True
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