## What is pseudo-polynomial time complexity?

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## What is pseudo-polynomial time complexity?

Pseudo-polynomial time complexity means polynomial in the value/magnitude of input but exponential in the size of input. By size we mean the number of bits required to write the input. From the pseudo-code of knapsack, we can find the time complexity to be O(nW).

### Is pseudo-polynomial P or NP?

For example, Dynamic Programming Solutions of 0-1 Knapsack, Subset-Sum and Partition problems are Pseudo-Polynomial. NP complete problems that can be solved using a pseudo-polynomial time algorithms are called weakly NP-complete.

#### What is complexity polynomial?

Definition. An algorithm is said to have polynomial time complexity if its worst-case running time Tworst(n) T worst ( n ) for an input of size n is upper bounded by a polynomial p(n) for large enough n≥n0 n ≥ n 0 .

**Is Fibonacci pseudo-polynomial time?**

1) Revisiting polynomial/ pseudo-polynomial/ exponential running times via Fibonacci numbers The recursive algorithm is (highly) exponential, the one where previously-computed values are stored in an array is pseudo-polynomial time, and the one that uses the closed-form expression for the n’th Fibonacci number is …

**How is knapsack pseudo polynomial?**

The running time is O(NW) for an unbounded knapsack problem with N items and knapsack of size W. W is not polynomial in the length of the input though, which is what makes it pseudo-polynomial.

## How do you find the complexity of a polynomial?

A naive way to evaluate a polynomial is to one by one evaluate all terms. First calculate x^n, multiply the value with cn, repeat the same steps for other terms and return the sum. Time complexity of this approach is O(n^2) if we use a simple loop for evaluation of x^n.

### Is O log n polynomial?

Yes, O(nlogn) is polynomial time. From http://mathworld.wolfram.com/PolynomialTime.html, An algorithm is said to be solvable in polynomial time if the number of steps required to complete the algorithm for a given input is O(n^m) for some nonnegative integer m, where n is the complexity of the input.

#### How is knapsack pseudo-polynomial?

**What is the time complexity of Dijkstra algorithm?**

Time Complexity of Dijkstra’s Algorithm is O ( V 2 ) but with min-priority queue it drops down to O ( V + E l o g V ) .