For this problem, you are only allowed to use standard python libraries

For this problem, you are only allowed to use standard python libraries. You may not use third-party libraries or call any shell/bash functions.

1 Problem 1

You are given a list of tuples of the form (<float> x, <float> y, <float> r) (let’s call these c-tup/es). Each c-tuple represents a circle on a rectangular coordinate space, with x and y being the coordinates of the center, and r being the radius. Assume that each c-tup/e has a unique radius.

Let a cluster of circles be a group of circles where each circle in the group overlaps with at least one other circle in that group. Formally, first let a path be formed between two circles when they overlap. Define a cluster as a group of n circles, where each circle is reachable from every other circle through the formed paths.

Write a python script that does the following: For each c/uster, the circle with the largest area is kept, and all other circles in that cluster are removed. Return the resulting list of c-tuples. Some examples are shown.

Input: [(0.5, 0.5, 0.5), (1.5, 1.5, 1.1), (0.7, 0.7, 0.4), (4, 4, 0.7)] Input: [(1.5, 1.5, 1.3), (4, 4, 0.7)] Input: [(1, 3, 0.7), (2, 3, 0.4), (3, 3, 0.9)]

_ Output: [(1.5, 1.5, 1.1), (4, 4, 0.7)] Output: [(1.5, 1.5, 1.3), (4, 4, 0.7)] | Output: [(3, 3, 0.9)]

Figure 1: The bottom left circles form a cluster Red circles are removed.

Figure 2: No clusters are found, and no circles are removed.

Figure 3: The three circles form a cluster. Red circles are removed.