Question

Write an algorithm that sorts n integers in the range 0 to n5 – 1 in O(n) time.
please answer it in 15 min, i'll upvote u

Answer 1

There are two algorithms whose time complexities are O(n) : Radix Sort and Counting Sort. As the given range on n in the question is quite high, Radix sort will be a better option to implement as it is faster for larger values.

Algorithm for Radix Sort:

• Step 1 - Define 10 queues each representing a bucket for each digit from 0 to 9.
• Step 2 - Consider the least significant digit of each number in the list which is to be sorted.
• Step 3 - Insert each number into their respective queue based on the least significant digit.
• Step 4 - Group all the numbers from queue 0 to queue 9 in the order they have inserted into their respective queues.
• Step 5 - Repeat from step 3 based on the next least significant digit.
• Step 6 - Repeat from step 2 until all the numbers are grouped based on the most significant digit.

Implementation of Radix Sort Algorithm using C Programming Language

#include <stdio.h>
#include <conio.h>
#include <stdlib.h>


int getMax(int list[], int n) {
    int mx = list[0];
    int i;
    for (i = 1; i < n; i++)
        if (list[i] > mx)
            mx = list[i];
    return mx;
}

void countSort(int list[], int n, int exp) {
    int output[n];
    int i, count[10] = { 0 };

    for (i = 0; i < n; i++)
        count[(list[i] / exp) % 10]++;

    for (i = 1; i < 10; i++)
        count[i] += count[i - 1];

    for (i = n - 1; i >= 0; i--) {
        output[count[(list[i] / exp) % 10] - 1] = list[i];
        count[(list[i] / exp) % 10]--;
    }

    for (i = 0; i < n; i++)
        list[i] = output[i];
}

void radixsort(int list[], int n) {
    int m = getMax(list, n);

    int exp;
    for (exp = 1; m / exp > 0; exp *= 10)
        countSort(list, n, exp);
}

void print(int list[], int n) {
    int i;
    for (i = 0; i < n; i++)
        printf("%d\t", list[i]);
}

int main()
{
    int list[] = { 82, 901, 100, 12, 150, 77, 55, 23 };
    int i, n = sizeof(list) / sizeof(list[0]);

    printf("List of numbers before sort: \n");
    for(i = 0; i<8; i++)
        printf("%d\t", list[i] );

    radixsort(list, n);

    printf("\n\nList of numbers after sort: \n");
    print(list, n);
    printf("\n\n");
    return 0;
}