Principle of combining mathematics

Principle of combining mathematics

In composite mathematics, content rejection is often used. We use content rejection to solve some composite numbers with conditions.

• Refresh principle: the number of elements with Properties A and B is equivalent to the number of elements with Properties A and B and the number of elements with both Properties A and B.
  The mathematical formula is represented as | A ∪ B | = | A | + | B |-| A ∩ B |.
  Graphical Representation
   
  The yellow area is what we want.
  Similarly, for the three properties, the mathematical formula is | A ∪ B ∪ C | = | A | + | B | + | C |-| A ∩ B |-| A ∩ C |-| B Branch C | + | A branch B Branch C |
  Why should we add the last one? This is because one more is subtracted during the subtraction process.

• For the principle of rejection, recursive and binary enumeration are commonly used. The biggest advantage of binary enumeration is to enumerate the subsets of all elements. Assume that there are m elements in a set, m is 1 or 0 for m-long binary numbers, for each 1
  -Corresponds to an element. The entire binary enumeration is all subsets, from 0 to 2 ^ m.

• Recursive Algorithms use the concept of dfs to search and retrieve each scheme for rejection. Because each question has a different search method, the same template is not used, so no code is required.

• In this case, all the odd and even properties are subtracted. If the requested properties are the opposite, the total number is subtracted.
• The principle of rejection is simple, and the actual situation is very complicated. Each question is rejected by a different nature, but the final idea remains unchanged, if you do more questions, you will gradually accumulate experience and finally get a good idea.