Pictured above are graphs representing algorithmic complexity of Big Oh notation functions. Assign the following labels to the appropriate graph. There will be two labels per graph. O(n) is done as an example. Dark Blue - Light Blue - Yellow Purple Green Brown Gray Big Oh notation O(n) Algorithmic growth linear

The Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. API specification. When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle whose sides are of the specified length. public static double height(double length) // Draws a filled equilateral…

Use the Java programming langauge if needed

Python: Graph Colouring A simple method to find a colouring of a graph, with vertices {0,1,…,?−1}, is the following greedy algorithm: For ? in 0, 1, 2, ..., n - 1: Find the smallest colour (positive integer) ? which is not a colour of any neighbour of ?. Assign ? as the colour of ?. i) Implement the method above as a function greedy_colouring which takes a networkx Graph G (with vertices {0,1,…,?−1}) and returns a list C of the colours of G, where C[i] is the colour of vertex ?. ii) As a test, the Hoffman-Singleton graph (nx.hoffman_singleton_graph()) should require 6 colours using this method. If you have a graph G, you can draw it with coloured vertices using the code below: ten_colours = ['#CC6677', '#332288', '#DDCC77', '#117733', '#88CCEE', '#882255', '#44AA99', '#999933', '#AA4499', '#DDDDDD'] nx.draw_networkx(G, node_color=[ten_colours[i - 1] for i in greedy_colouring(G)], with_labels=False) iii) One way of refining the…