Why does radix sort work

Sorting is performed from least significant digit to the most significant digit. Radix sort algorithm requires the number of passes which are equal to the number of digits present in the largest number among the list of numbers.

For example, if the largest number is a 3 digit number then that list is sorted with 3 passes. To sort an unsorted list with 'n' number of elements, Radix sort algorithm needs the following complexities The perfect place for easy learning Linked List Data Structure.

Hash Table Data Structure. Dynamic Programming. Explore Python Examples. Popular Examples Add two numbers. Check prime number. Find the factorial of a number. Print the Fibonacci sequence. Check leap year. DSA Introduction What is an algorithm? Related Topics Counting Sort Algorithm. Working of Radix Sort Please go through the counting sort before reading this article because counting sort is used as an intermediate sort in radix sort.

Working of Radix Sort Find the largest element in the array, i. Let X be the number of digits in max. X is calculated because we have to go through all the significant places of all elements.

In this array [, , , 23, 1, 45, ] , we have the largest number Let us first limit k. In that case, the complexity becomes O nLogb n. What if we make value of b larger?. What should be the value of b to make the time complexity linear? If we set b as n, we get the time complexity as O n.

In other words, we can sort an array of integers with range from 1 to nc if the numbers are represented in base n or every digit takes log2 n bits. Radix Sort takes advantage of the following ideas: Number of digits in an Integer is determined by: its base very less compared to the data Numbers increase linearly but number of digits increase logarithmically. Why does sorting one digit place at a time work in Radix Sort?