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Polynomial vs non polynomial time complexity

Q: What is the difference between polynomial and non polynomial time complexity?

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Algorithms which have exponential time complexity grow much faster than polynomial algorithms. The difference you are probably looking for happens to be where the variable is in the equation that expresses the run time. Equations that show a polynomial time complexity have variables in the bases of their terms. Examples: n^3 + 2n^2 + 1. Notice n is in the base, NOT the exponent. In exponential equations, the variable is in the exponent. Examples: 2^n. As said before, exponential time grows much faster. If n is equal to 1000 (a reasonable input for an algorithm), then notice 1000^3 is 1 billion, and 2^1000 is simply huge! For a reference, there are about 2^80 hydrogen atoms in the sun, this is much more than 1 billion.

That means that the running time of a program is proportional to some power of the input size.

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The difference between multicollinearity and auto correlation is that multicollinearity is a linear relationship between 2 or more explanatory variables in a multiple regression while while auto-correlation is a type of correlation between values of a process at different points in time, as a function of the two times or of the time difference.

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P is the class of problems for which there is a deterministic polynomial time algorithm which computes a solution to the problem. NP is the class of problems where there is a nondeterministic algorithm which computes a solution to the problem, but no known deterministic polynomial time solution

A problem is 'in NP' if there exists a polynomial time complexity algorithm which runs on a Non-Deterministic Turing Machine that solves it. A problem is 'NP Hard' if all problems in NP can be reduced to it in polynomial time, or equivalently if there is a polynomial-time reduction of any other NP Hard problem to it. A problem is NP Complete if it is both in NP and NP hard.

Algorithms which have exponential time complexity grow much faster than polynomial algorithms. The difference you are probably looking for happens to be where the variable is in the equation that expresses the run time. Equations that show a polynomial time complexity have variables in the bases of their terms. Examples: n^3 + 2n^2 + 1. Notice n is in the base, NOT the exponent. In exponential equations, the variable is in the exponent. Examples: 2^n. As said before, exponential time grows much faster. If n is equal to 1000 (a reasonable input for an algorithm), then notice 1000^3 is 1 billion, and 2^1000 is simply huge! For a reference, there are about 2^80 hydrogen atoms in the sun, this is much more than 1 billion.

That means that the running time of a program is proportional to some power of the input size.

Algorithms which have exponential time complexity grow much faster than polynomial algorithms. The difference you are probably looking for happens to be where the variable is in the equation that expresses the run time. Equations that show a polynomial time complexity have variables in the bases of their terms. Examples: n^3 + 2n^2 + 1. Notice n is in the base, NOT the exponent. In exponential equations, the variable is in the exponent. Examples: 2^n. As said before, exponential time grows much faster. If n is equal to 1000 (a reasonable input for an algorithm), then notice 1000^3 is 1 billion, and 2^1000 is simply huge! For a reference, there are about 2^80 hydrogen atoms in the sun, this is much more than 1 billion.

NP stands for Nondeterministic Polynomial time, and is a class of complexity of problems. A problem is in NP if the computing time needed grows exponentially with the amount of input, but it only takes polynomial time to determine if a given solution is correct or not.It is called nondeterministic because a computer that always automatically chooses the right course of action in each step would come up with a correct solution in polynomial time.

Do you mean, "the difference between an algorithm that runs in polynomial time, and one that runs in exponential time".First a real quick review. A polynomial is any equation of the formy = cmxm + ... + c2x2 + c1x + c0 ,where ci are constantsAn exponential function is something of the formy = cxThese functions grow much faster than any polynomial function.So, if T(n) describes the runtime of an algorithm as a function of whatever (# of inputs, size of input, etc.)., and T(n) can be bound above by any polynomic function, then we say that algorithm runs in polynomial time.If it can't be bound above by a polynomial function, but can be bound above by an exponential function, we say it runs in exponential time.Note how ugly an exponential algorithm is. By adding one more input, we roughly double (or triple, whatever c is) the run-time.

In computer science, P typically refers to the complexity class of decision problems that can be solved in polynomial time by a deterministic Turing machine. Problems in this class are considered tractable and efficiently solvable within a reasonable time frame.

time complexity is 2^57..and space complexity is 2^(n+1).

"Running Time" is essentially a synonym of "Time Complexity", although the latter is the more technical term. "Running Time" is confusing, since it sounds like it could mean "the time something takes to run", whereas Time Complexity unambiguously refers to the relationship between the time and the size of the input.

There is no time difference between them.

there is no difference between the time of the two cities