The running time of Counting Sort is pseudo-polynomial in input size n for a given array A[1..n] of integers. O True O False

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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**Question:**

The running time of Counting Sort is pseudo-polynomial in input size \( n \) for a given array \( A[1 \ldots n] \) of integers.

- \( \circ \) True
- \( \circ \) False

**Analysis:**

This question asks about the complexity of Counting Sort. Typically, Counting Sort runs in \( O(n + k) \) time, where \( n \) is the number of elements in the array, and \( k \) is the range of the input. In this context, the term "pseudo-polynomial" refers to an algorithm that runs in polynomial time with respect to the numerical value of the input, rather than the size of the input description. 

Counting Sort is not pseudo-polynomial with respect to \( n \) alone because it also depends on \( k \), which is not necessarily polynomially related to \( n \).
Transcribed Image Text:**Question:** The running time of Counting Sort is pseudo-polynomial in input size \( n \) for a given array \( A[1 \ldots n] \) of integers. - \( \circ \) True - \( \circ \) False **Analysis:** This question asks about the complexity of Counting Sort. Typically, Counting Sort runs in \( O(n + k) \) time, where \( n \) is the number of elements in the array, and \( k \) is the range of the input. In this context, the term "pseudo-polynomial" refers to an algorithm that runs in polynomial time with respect to the numerical value of the input, rather than the size of the input description. Counting Sort is not pseudo-polynomial with respect to \( n \) alone because it also depends on \( k \), which is not necessarily polynomially related to \( n \).
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