There are a set of schools and houses in a city. You need to group the...

   

 

 

 

   

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There are a set of schools and houses in a city. You need to group the houses into school zones. The zone for each school is defined as a circle with a 3km radius. That means, any house that has a radial distance less than or equal to 3km from the school is considered to be in the school zone. y). See the The location of each school and each house is specified using their coordinates, (x,y). See the below map as an example (not to scale). x S(1.5,7) x H7(0.5,6.8) XH6(4,8) x H (12,6.5) x H(8,7.5) X S3 (10,5) X H3(1,2) x S(1,1) x H(0.5,0.3) x H5(3,6) x H,(9,4.5) X H(9.5,1) The list of tuples schools contains the locations (coordinates) of the schools. The list of tuples houses contains the locations (coordinates) of the houses. You will be solving this problem in 3 steps as outlined in the 3 sub-parts of this question below. Note: The above map is just an example. Your codes should work for any map with the same format. Make sure you reuse any functions written in the previous parts (of this question) wherever possible, without re-writing the same code. 20a) Write a function that takes in the coordinates of two points and returns the Euclidean distance between them (rounded to 2 decimal places). The Euclidean distance, D, is calculated using the following formula: D = (x1 = x2)+(y1 - y2) - where (X1,Y1) and (x2,Y2) are the coordinates of the two points. (2 marks) def distance(point1,point2): Inputs: Two tuples containing the coordinates of two points Output: The Euclidean distance between the two points, rounded to 2 decimal places Examples: >>> distance((1,3),(2,4)) 1.41 >>> distance((0,5),(2.5)) 2.0 >>> distance((0,0), (3,4)) 5.0 20b) Write a function that returns True if the distance between two points is less than or equal to 3 units. This function can be used to determine if a given house is within the zone of a given school. Make sure you reuse the code written in part (a) above. (4 marks) def within_zone(point1.point2): Inputs: Two tuples containing the coordinates of two points Output: True if the distance between two points is less than or equal to 3 units, False otherwise Examples: >>> within_zone((1,3),(2,4)). True >>> within_zone((0,0), (3,4)) False >>> within_zone((2.5,6.3),(4,7.2)) True 20c) Write a function that will group the houses within each school zone based on the following criteria. For each school create a list of houses within its zone (within 3km). If a house is within 3km from more than one school add that house to the lists of all those schools. If a house does not fall within 3km of any of the schools, that house needs to be added to the list of the nearest school. Your function needs to take in two lists of tuples, one containing the locations of the schools and the other containing the locations of the houses. The output from the function should be a table, with each row corresponding to each school and the inner lists containing the house locations (tuples) that are within the zone for each school. For example, in your output table, row 0 contains the locations of houses that are within the zone for school 0, row 1 contains the locations of houses that are within the zone for school 1 and so on. rmat of t (4marks) Refer to the examples below (in doctests) for the format of the output. (4 marks) er to the examples below (in doctests) for the f def group_zones(schools,houses): Inputs: Two lists of tuples containing the locations (coordinates) of schools and houses. Output: A table contaning the list of houses that belong to each school zone. Examples: >>> schools = [(1,1),(1.5,7),(10,5)] >>> houses = [(0.5,0.3),(8,7.5), (1,2).(9.5,1),(3,6),(4,8). (0.5,6.8),(12,6.5),(9,4.5)] >>>group_zones(schools, houses) [[(0.5, 0.3), (1, 2)]. [(3, 6), (4, 8), (0.5, 6.8)]. [(12, 6.5), (9,4.5), (8, 7.5), (9.5, 1)]] >>> schools = [(0,0),(2,2)] >>> houses = [(1,0.5),(1,3.5),(0.2,1.5)] >>> group_zones (schools, houses) [[(1,0.5), (0.2, 1.5)], [(1,0.5), (1, 3.5), (0.2, 1.5)]] There are a set of schools and houses in a city. You need to group the houses into school zones. The zone for each school is defined as a circle with a 3km radius. That means, any house that has a radial distance less than or equal to 3km from the school is considered to be in the school zone. y). See the The location of each school and each house is specified using their coordinates, (x,y). See the below map as an example (not to scale). x S(1.5,7) x H7(0.5,6.8) XH6(4,8) x H (12,6.5) x H(8,7.5) X S3 (10,5) X H3(1,2) x S(1,1) x H(0.5,0.3) x H5(3,6) x H,(9,4.5) X H(9.5,1) The list of tuples schools contains the locations (coordinates) of the schools. The list of tuples houses contains the locations (coordinates) of the houses. You will be solving this problem in 3 steps as outlined in the 3 sub-parts of this question below. Note: The above map is just an example. Your codes should work for any map with the same format. Make sure you reuse any functions written in the previous parts (of this question) wherever possible, without re-writing the same code. 20a) Write a function that takes in the coordinates of two points and returns the Euclidean distance between them (rounded to 2 decimal places). The Euclidean distance, D, is calculated using the following formula: D = (x1 = x2)+(y1 - y2) - where (X1,Y1) and (x2,Y2) are the coordinates of the two points. (2 marks) def distance(point1,point2): Inputs: Two tuples containing the coordinates of two points Output: The Euclidean distance between the two points, rounded to 2 decimal places Examples: >>> distance((1,3),(2,4)) 1.41 >>> distance((0,5),(2.5)) 2.0 >>> distance((0,0), (3,4)) 5.0 20b) Write a function that returns True if the distance between two points is less than or equal to 3 units. This function can be used to determine if a given house is within the zone of a given school. Make sure you reuse the code written in part (a) above. (4 marks) def within_zone(point1.point2): Inputs: Two tuples containing the coordinates of two points Output: True if the distance between two points is less than or equal to 3 units, False otherwise Examples: >>> within_zone((1,3),(2,4)). True >>> within_zone((0,0), (3,4)) False >>> within_zone((2.5,6.3),(4,7.2)) True 20c) Write a function that will group the houses within each school zone based on the following criteria. For each school create a list of houses within its zone (within 3km). If a house is within 3km from more than one school add that house to the lists of all those schools. If a house does not fall within 3km of any of the schools, that house needs to be added to the list of the nearest school. Your function needs to take in two lists of tuples, one containing the locations of the schools and the other containing the locations of the houses. The output from the function should be a table, with each row corresponding to each school and the inner lists containing the house locations (tuples) that are within the zone for each school. For example, in your output table, row 0 contains the locations of houses that are within the zone for school 0, row 1 contains the locations of houses that are within the zone for school 1 and so on. rmat of t (4marks) Refer to the examples below (in doctests) for the format of the output. (4 marks) er to the examples below (in doctests) for the f def group_zones(schools,houses): Inputs: Two lists of tuples containing the locations (coordinates) of schools and houses. Output: A table contaning the list of houses that belong to each school zone. Examples: >>> schools = [(1,1),(1.5,7),(10,5)] >>> houses = [(0.5,0.3),(8,7.5), (1,2).(9.5,1),(3,6),(4,8). (0.5,6.8),(12,6.5),(9,4.5)] >>>group_zones(schools, houses) [[(0.5, 0.3), (1, 2)]. [(3, 6), (4, 8), (0.5, 6.8)]. [(12, 6.5), (9,4.5), (8, 7.5), (9.5, 1)]] >>> schools = [(0,0),(2,2)] >>> houses = [(1,0.5),(1,3.5),(0.2,1.5)] >>> group_zones (schools, houses) [[(1,0.5), (0.2, 1.5)], [(1,0.5), (1, 3.5), (0.2, 1.5)]]