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# Difference between Deterministic and Non-deterministic Algorithms

In the context of programming, an **Algorithm** is a set of well-defined instructions in sequence to perform a particular task and achieve the desired output. Here we say "a set of defined instructions" which means that somewhere the user knows the outcome of those instructions if they get executed in the expected manner.

On the basis of the knowledge about outcome of the instructions, there are two types of algorithms namely, **Deterministic** and **Non-deterministic Algorithms**.

Read this article to learn more about deterministic and non-deterministic algorithms and how they are different from each other.

## What is Deterministic Algorithm?

A **deterministic algorithm** is a type of algorithm in which the result of every algorithm is uniquely defined. Hence, a deterministic algorithm performs fixed number of steps and always get finished with accept or reject state with the same result. The target machine executes the same instruction and gives the same results that does not depend upon the way or process in which the instruction gets executed.

Deterministic algorithms can solve a problem in polynomial time. A deterministic algorithm always has a single outcome, i.e. the input given to it always results the same output. A mathematical function is a common example of the deterministic algorithm.

## What is Non-Deterministic Algorithm?

A **non-deterministic algorithm** is one in which the output of every algorithm is not uniquely defined and thus the result could be random. Hence, the non-deterministic algorithms have multiple outcomes.

Non-deterministic algorithms take multiple execution paths, thus it is quite difficult to determine the next state of the machine. Unlike deterministic algorithms, a non-deterministic algorithm cannot solve problems in polynomial time. Random functions are examples of nondeterministic algorithms.

## Difference between Deterministic and Non-deterministic Algorithms

The following are the main differences between deterministic and non-deterministic algorithms −

Key |
Deterministic Algorithm |
Non-deterministic Algorithm |
---|---|---|

Definition |
The algorithms in which the result of every algorithm is uniquely defined are known as the Deterministic Algorithm. In other words, we can say that the deterministic algorithm is the algorithm that performs fixed number of steps and always get finished with accept or reject state with the same result. |
The algorithms in which the result of every algorithm is not uniquely defined and result could be random are known as the Non-Deterministic Algorithm. |

Execution |
In Deterministic Algorithms execution, the target machine executes the same instruction and results same outcome which is not dependent on the way or process in which instruction get executed. |
In case of Non-Deterministic Algorithms, the machine executing each operation is allowed to choose any one of these outcomes subjects to a determination condition to be defined later. |

Type |
On the basis of execution and outcome in case of Deterministic algorithm, they are also classified as reliable algorithms as for a particular input instructions the machine will give always the same output. |
Nondeterministic algorithms are classified as non-reliable algorithms for a particular input the machine will give different output on different executions. |

Execution Time |
As the outcome is known and is consistent on different executions, so Deterministic algorithms take a polynomial time for their execution. |
As the outcome is not known and is non-consistent on different executions, so Non-Deterministic algorithms cannot get executed in polynomial time. |

Execution path |
In deterministic algorithms, the path of execution for algorithm is same in every execution. |
In case of Non-Deterministic algorithms, the path of execution is not same for algorithm in every execution and could take any random path for its execution. |

## Conclusion

The most significant difference between these two types of algorithms is that a deterministic algorithm has the same path of execution for every execution, whereas a non-deterministic algorithm can take any random path of execution for different executions.