Pseudo-polynomial Algorithms

• Difficulty Level : Easy
• Last Updated : 22 Aug, 2021

What is a pseudo-polynomial algorithm?
A pseudo-polynomial algorithm is an algorithm whose worst-case time complexity is polynomial in the numeric value of input (not number of inputs).
For example, consider the problem of counting frequencies of all elements in an array of positive numbers. A pseudo-polynomial time solution for this is to first find the maximum value, then iterate from 1 to maximum value and for each value, find its frequency in array. This solution requires time according to maximum value in input array, therefore pseudo-polynomial. On the other hand, an algorithm whose time complexity is polynomial in the number of elements in array (not value) is considered as polynomial time algorithm.

Pseudo-polynomial and NP-Completeness
Some NP-Complete problems have pseudo-polynomial time solutions. 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.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

StackOverflow – What is pseudopolynomial time? How does it differ from polynomial time? (top answer)

This article is contributed by Dheeraj Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.