def count_crossings_and_nestings(arcs): n = len (arcs) // 2 crossings = 0 nestings = 0 for i in range(2 * n): for j in range(i + 1, 2 * n): if arcs [i] [0] < arcs [j] [0] < arcs [i] [1] < arcs [j] [1]: crossings += 1 elif arcs [i] [0] > arcs [j] [0] > arcs[i] [1] > arcs[j][1]: crossings += 1 elif arcs[i][0] < arcs [j] [0] < arcs [j] [1] < arcs [i] [1]: nestings += 1 elif arcs [i] [0] > arcs [j] [0] > arcs [i] [1] > arcs [j][1]: nestings += 1 return crossings, nestings #Test cases test_cases=[ [], [(0,1)], [(0,1),(2,3)], [(0,3), (1,2)], [(0,2), (1,3)] ] # Empty set of arcs # Single arc # Two non-overlapping arcs # Two overlapping arcs # Two nested arcs for i, arcs in enumerate(test_cases, 1): crossings, nestings = count_crossings_and_nestings(arcs) print (f"Test case {i}:") print (f"Number of arcs: {len(arcs)}") print (f"Number of crossings: {crossings}") print (f"Number of nestings: {nestings}") print() Explanation below: {} (empty set of arcs): The output can be defined as (0, 0). {(0, 1)} (single arc): The output can be defined as (0, 0) because there are no crossings or nestings. {(0, 1), (2, 3)} (two non-overlapping arcs): The output can be defined as (0, 0) because there are no crossings or nestings. {(0, 3), (1, 2)} (two overlapping arcs): The output can be defined as (1, 0) because there is one crossing but no nestings. {(0, 2), (1, 3)} (two nested arcs): The output can be defined as (0, 1) because there are no crossings but one nesting. The output matches the expectations for all the test cases. Therefore, the function is working.

Hi, I've been trying to solve this problem to drawCircle using Python and Mindtap. Define a function main that will draw a circle with the following parameters when the program is run: X = 50 Y = 75 Radius = 100 import turtle import math def draw_circle(radius, x, y):     turtle.up()     turtle.goto(x, y + radius)     turtle.down()     for i in range(120):         turtle.forward(2 * math.pi * radius/120.0)         turtle.right(3.0)     return     draw_circle(100, 25, 75)   answer is giving me 0.04% difference

Using the C Programming language, write a program that sums an array of 50 elements. Next,optimize the code using loop unrolling. Loop unrolling is a program transformation that reduces thenumber of iterations for a loop by increasing the number of elements computed on each iteration.Generate a graph of performance improvement.

For diagrams with three arcs, there are 15 possibilities. considering the following set of arcs: arcs = [(0, 1), (0, 2), (1, 2)] This set of arcs should result in 1 crossing and 2 nestings. However, let's check the function's output: crossings, nestings = count_crossings_and_nestings(arcs)print(f"Number of crossings: {crossings}")print(f"Number of nestings: {nestings}") This outputs: Number of crossings: 0Number of nestings: 0 My questions I need help from you: The first problem is related to the variable n and its value. Explain what goes wrong. Provide a better implementation of the function, avoiding the use of n. Use the same function name, i.e., count_crossings_and_nestings.