课程 9. Sets

难度：

Pythonlib

任务«在密码学中查找简单数字»

💻 Python

你需要开发一个程序，用于确定给定范围内的质数，并将它们保存在集合中。在现代世界中，质数在密码学中扮演着重要角色，确保数据传输的安全性。你的任务是帮助研究人员生成一组质数，以测试新的加密算法。

输入格式

两个整数，分别表示范围的起始和结束（包含两端），每个整数占一行

输出格式

在给定范围内找到的所有简单数字，按升序排列，集合中的元素用空格分隔

示例

输入

2
10

输出

2 3 5 7

提示

Comparing sets

Subset

A set A is a subset of set B if all elements of set A, without exception, are also contained in set B. The issubset() method is used to check this condition. and the operator .

A useful tip: The <= operator checks for a "non-strict" subset. This means that any set is a subset of itself (set1<= set1 returns True). If you need to check that the set A is a subset of B, but it is not equal to it, use the strict inequality operator .

set1 = {1, 2}
set2 = {1, 2, 3}
set3 = {1, 2}

# Checking for a subset
print(set1.issubset(set2))  # Output: True
print(set1 <= set2) # Output: True

# Checking for a strict subset
print(set1 < set2) # Output: True
print(set3< set1) # Output: False, since the sets are equal

Superset

A set A is a superset of set B if it contains all the elements that are in set B. The issuperset() method is used for verification. and the operator =.

A useful tip: Similarly to subsets, the = operator checks for a "non-strict" superset. To check for a strict superset (A contains all the elements of B and at least one additional one), use the operator.

set1 = {1, 2, 3}
set2 = {1, 2}

# Checking for a superset
print(set1.issuperset(set2))  # Output: True
print(set1 >= set2) # Output: True

# Checking for a strict superset
print(set1 > set2) # Output: True
print(set1 > {1, 2, 3}) # Conclusion: False, since the sets are equal

Equality of sets

Sets are considered equal if they contain exactly the same set of elements. The order of the elements does not matter at all. The == operator is used for verification.

set1 = {1, 2, 3}
set2 = {3, 2, 1}
set3 = {1, 2, 3, 3} # The duplicate will be ignored when creating a set.

print(set1 == set2) # Output: True
print(set1 == set3) # Output: True

Other set methods

Copying a set

The copy() method returns a surface copy of the set.

Important advice: Do not confuse copying with assignment. If you write set2 = set1, then set2 will not be a new set, but only another reference to set1. Changing set2 will change set1. Use copy() to create an independent array.

set1 = {1, 2, 3}

# Correct copying
set2 = set1.copy()
set2.add(4)
print(f"Original set1: {set1}")  # Output: Original set1: {1, 2, 3}
print(f"Copy of set2: {set2}")    # Output: A copy of set2: {1, 2, 3, 4}

# Incorrect copying (link assignment)
set3 = set1
set3.add(5)
print(f"Original set1 after changing set3: {set1}") # Output: Original set1 after changing set3: {1, 2, 3, 5}
print(f"Reference set3: {set3}")                       # Output: set3 link: {1, 2, 3, 5}

Updating the set

The update() method adds to the current set all the elements from another set or any other iterable object (for example, a list or a tuple). The method modifies the original set and returns nothing (None).

set1 = {1, 2, 3}
set2 = {3, 4, 5}
list1 = [5, 6, 7]

set1.update(set2) # Duplicate {3} will be ignored
print(set1) # Output: {1, 2, 3, 4, 5}

set1.update(list1) # You can update it from the list
print(set1) # Output: {1, 2, 3, 4, 5, 6, 7}

Sets and their applications

Arrays are extremely useful in various tasks due to their speed and unique properties. They are ideal for removing duplicates, quickly checking for an element, and performing mathematical operations (union, intersection, difference).

Removing duplicates from the list

This is one of the most common uses of arrays. Converting a list to a set automatically removes all duplicates. Then, if necessary, the set can be converted back to a list.

It is important to remember: With this transformation, the original order of the list items is not preserved.

numbers = [1, 2, 2, 3, 4, 4, 5, 1]
unique_numbers = list(set(numbers))
print(unique_numbers) # The output can be [1, 2, 3, 4, 5] ( the order is not guaranteed)

Search for common items in two lists

To find the elements that are present in both collections, you can transform them into sets and use the intersection operator &.

list1 = [1, 2, 3, 4]
list2 = [3, 4, 5, 6]
common_elements = list(set(list1) & set(list2))
print(common_elements)  # Output: [3, 4] (order is not guaranteed)

Search for unique elements (symmetric difference)

To find the elements that are in one of the lists, but not both at once, use the symmetric difference operator ^.

list1 = [1, 2, 3, 4]
list2 = [3, 4, 5, 6]
unique_to_each_list = list(set(list1) ^ set(list2))
print(unique_to_each_list) # Output: [1, 2, 5, 6] ( the order is not guaranteed)