This is a Python program to find smallest set of unit-length closed intervals that contains all points using greedy algorithm.

We are given a set of points on the x-axis. We have to find the minimum number of closed intervals of length 1 that will contain all of these points.

1. The function smallest_unit_length_intervals is defined.

2. It takes a list points as argument.

3. points is a list of numbers that represent points on the x-axis.

4. The list points is first sorted in ascending order.

5. The algorithm works by first including the closed interval [p, p + 1] where p is the rightmost point (i.e. the point with the smallest value).

6. All the points that are included within this interval are discarded.

7. The next rightmost point q is selected and the closed interval [q, q + 1] is included.

8. The above process continues until there are no remaining points.

9. The solution set is returned which is the smallest-size set of closed intervals that contain all the given points.

Here is the source code of a Python program to find smallest set of unit-length closed smallest_unit_length_intervals that contains all points using greedy algorithm. The program output is shown below.

def smallest_unit_length_intervals(points): """Return smallest set with unit-length intervals that includes all points. A smallest set containing closed intervals is returned such that each point is included in some interval. The intervals are in the form of tuples (a, b). points is a list of points on the x-axis. """ points.sort() smallest_set = set() end_of_last_interval = float('-inf') for p in points: if end_of_last_interval <= p: interval = (p, p + 1) smallest_set.add(interval) end_of_last_interval = p + 1 return smallest_set points = input('Enter the points: ').split() points = [float(p) for p in points] ans = smallest_unit_length_intervals(points) print('A smallest-size set containing unit-length intervals ' 'that contain all of these points is', ans)

1. The user is prompted to enter the points.

2. The function smallest_unit_length_intervals is called on these points to get the smallest-size set containing unit-length intervals that contain all the given points.

3. This set is then displayed.

Case 1: Enter the points: 1 1.5 1.8 2.1 2.2 3.4 4.5 5.6 5.9 A smallest-size set containing unit-length intervals that contain all of these points is {(1.0, 2.0), (4.5, 5.5), (2.1, 3.1), (3.4, 4.4), (5.6, 6.6)} Case 2: Enter the points: 2.1 10.3 11.2 A smallest-size set containing unit-length intervals that contain all of these points is {(10.3, 11.3), (2.1, 3.1)} Case 3: Enter the points: 5 A smallest-size set containing unit-length intervals that contain all of these points is {(5.0, 6.0)}

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