#Minimum Length Triangulation






# Example usage
    # Example points

    # Example maximum length

    # Calculate the minimum length triangulation

    # Check if it satisfies the maximum length constraint

    # Print the result


if __name__ == '__main__':
    import math
    def distance(point1, point2):
        x1, y1 = point1
        x2, y2 = point2
        return math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)
    def minimum_length_triangulation(points):
        n = len(points)
        dp = [[0] * n for _ in range(n)]
        for gap in range(2, n):
            for i in range(n - gap):
                j = i + gap
                dp[i][j] = math.inf
                for k in range(i + 1, j):
                    cost = dp[i][k] + dp[k][j] + distance(points[i], points[k]) + distance(points[k], points[j])
                    dp[i][j] = min(dp[i][j], cost)
        return dp[0][n - 1]
    if __name__ == '__main__':
        points = [(0, 0), (1, 0), (0, 1), (1, 1)]
        maximum_length = 3.0
        minimum_length = minimum_length_triangulation(points)
        result = minimum_length <= maximum_length
        if result:
            print("A triangulation with total length", minimum_length, "or less exists.")
        else:
            print("No triangulation with the given maximum length constraint exists.")
