Answer:
O(N!), O(2N), O(N2), O(N), O(logN)
Explanation:
N! grows faster than any exponential functions, leave alone polynomials and logarithm. so O( N! ) would be slowest.
2^N would be bigger than N². Any exponential functions are slower than polynomial. So O( 2^N ) is next slowest.
Rest of them should be easier.
N² is slower than N and N is slower than logN as you can check in a graphing calculator.
NOTE: It is just nitpick but big-Oh is not necessary about speed / running time ( many programmers treat it like that anyway ) but rather how the time taken for an algorithm increase as the size of the input increases. Subtle difference.
No, it is not necessary that variables that contain numbers should always be declared as integer or floating-point data types.
It is not necessary that variables that contain numbers should be declared as integer and floating point data types. Because number can be declared with different data types. As we know that data type is a vital aspect in programming. It describes the type of a value that is contained in a variable. It is the data type based on which memory is allocated to a number or any type of variables.
Numbers can be whole decimal/fractional, signed, unsigned, small, and long. Simply, they exist in a variety of values. According to their values range, the amount of memory is reserved.
Different programming languages offer different data types to store numbers, depending on their types and size. Let’s consider some examples of data types used in programming languages in order to declare variables holding numbers.
- In Python int, float, and complex are the data types used to declare number type variables.
- SQL uses INTEGER, SMALLINT , BIGINT , NUMERIC() , and DECIMAL() data types for numbers.
- To deal with number type variables, Java has six predefined data types, such as int, long, short, byte, float, and double.
- JavaScript uses a single data type called 'number' to declare numbers.
- In C++, two fundamental data types, int and float, are used to represent numeric variables. But C++ is not only limited to these two data types. The data type char can also store numbers. Other data types for declaring numbers as variables are derived from int, float and char, such as short int, long int, signed int, unsigned int, double, long double, signed char, unsigned char etc. etc.
So in concluding remarks, declaring a number type variable is not only limited to using integers and floating-points data types. Rather it entirely depends on the respective programming language, and size and type of the number to be stored in the variable.
You can learn more about data types at
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