Program to check whether list of points form a straight line or not in Python

Suppose we have a list of coordinates in a Cartesian plane, we have to check whether the coordinates form a straight line segment or not.

So, if the input is like coordinates = [(5, 5), (8, 8), (9, 9)], then the output will be True, as these points are forming a line segment with a slope 1.

Algorithm

To solve this, we will follow these steps −

• (x0, y0) := coordinates[0]
• (x1, y1) := coordinates[1]
• for i in range 2 to size of coordinates list - 1, do
  • (x, y) := coordinates[i]
  • if (x0 - x1) * (y1 - y) is not same as (x1 - x) * (y0 - y1), then
    • return False
• return True

How It Works

The algorithm uses the cross product method to check collinearity. For three points to be collinear, the slope between any two pairs of points must be the same. Instead of calculating slopes directly (which can cause division by zero), we use cross multiplication: (x0 - x1) * (y1 - y) == (x1 - x) * (y0 - y1).

Example

Let us see the following implementation to get better understanding −

class Solution:
    def solve(self, coordinates):
        (x0, y0), (x1, y1) = coordinates[0], coordinates[1]
        for i in range(2, len(coordinates)):
            x, y = coordinates[i]
            if (x0 - x1) * (y1 - y) != (x1 - x) * (y0 - y1):
                return False
        return True

ob = Solution()
coordinates = [[5, 5], [8, 8], [9, 9]]
print(ob.solve(coordinates))

True

Testing with Non-Collinear Points

class Solution:
    def solve(self, coordinates):
        (x0, y0), (x1, y1) = coordinates[0], coordinates[1]
        for i in range(2, len(coordinates)):
            x, y = coordinates[i]
            if (x0 - x1) * (y1 - y) != (x1 - x) * (y0 - y1):
                return False
        return True

ob = Solution()
# Test with points that don't form a straight line
coordinates = [[1, 2], [2, 3], [3, 5]]
print(ob.solve(coordinates))

False

Simplified Function Approach

def check_straight_line(coordinates):
    if len(coordinates) < 3:
        return True
    
    (x0, y0), (x1, y1) = coordinates[0], coordinates[1]
    
    for i in range(2, len(coordinates)):
        x, y = coordinates[i]
        if (x0 - x1) * (y1 - y) != (x1 - x) * (y0 - y1):
            return False
    return True

# Test cases
print(check_straight_line([[1, 2], [2, 3], [3, 4]]))  # True
print(check_straight_line([[1, 1], [2, 2], [3, 4]]))  # False

True
False

Conclusion

The cross product method efficiently checks if points are collinear by avoiding division and handling vertical lines. This algorithm has O(n) time complexity and works reliably for all coordinate configurations.