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Implement Sorting of Less than 100 Numbers in O(n) Complexity



Implement Sorting of Less than 100 Numbers in O(n) Complexity

This is a C++ Program to Sort the Numbers lesser than 100 in O(n) Complexity.

- We can implement the task best using Radix sort.
- In this algorithm sorting of data is done from least significant digit to most significant digit.
- Here we need 10 different spaces labeled 0 to 9.
- Assume we have 'n' number of inputs.
- Let 'd' be the maximum number of digit the input data has, here d can have values either 1 or 2 or 3.
- The time complexity for radix sort is O(n*3) that is O(n).
- Radix sort solves the problem of card sorting by sorting on the least significant digit first.

- Get the maximum value from the input array which has 'd' digits.
- Starting from least significant digit, sort the data.
- Take this data as input for next significant digit.
- Run the iteration till d digit.
- Display the result.
- Exit.

C++ program to Sort the Numbers lesser than 100 in O(n) Complexity using Radix Sort.

#include <iostream>
 
using namespace std;
 
// Get maximum value from array.
int getMax(int arr[], int n)
{
	int max = arr[0];
	for (int i = 1; i < n; i++)
		if (arr[i] > max)
			max = arr[i];
	return max;
}
 
// Count sort of arr[].
void countSort(int arr[], int n, int exp)
{
	// Count[i] array will be counting the number of array values having that 'i' digit at their (exp)th place.  
	int output[n], i, count[10] = {0};
 
	// Count the number of times each digit occurred at (exp)th place in every input.
	for (i = 0; i < n; i++)
		count[(arr[i] / exp) % 10]++;
 
	// Calculating their cumulative count.
	for (i = 1; i < 10; i++)
		count[i] += count[i-1];
 
	// Inserting values according to the digit '(arr[i] / exp) % 10' fetched into count[(arr[i] / exp) % 10].
	for (i = n - 1; i >= 0; i--)
	{
		output[count[(arr[i] / exp) % 10] - 1] = arr[i];
		count[(arr[i] / exp) % 10]--;
	}
 
	// Assigning the result to the arr pointer of main().
	for (i = 0; i < n; i++)
		arr[i] = output[i];
}
 
// Sort arr[] of size n using Radix Sort.
void radixsort(int arr[], int n)
{
	int exp, m;
	m = getMax(arr, n);
 
	// Calling countSort() for digit at (exp)th place in every input.
	for (exp = 1; m/exp > 0; exp *= 10)
		countSort(arr, n, exp);
}
 
int main()
{
	int n, i;
	cout<<"\nEnter the number of data element to be sorted: ";
	cin>>n;
 
	int arr[n];
	for(i = 0; i < n; i++)
	{
		cout<<"Enter element "<<i+1<<": ";
		cin>>arr[i];
	}
 
	radixsort(arr, n);
 
	// Printing the sorted data.
	cout<<"\nSorted Data ";
	for (i = 0; i < n; i++)
		cout<<"->"<<arr[i];
	return 0;
}