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**Introduction To Algorithm**

The word **Algorithm** means “a process or set of rules to be followed in calculations or other problem-solving operations”. Therefore Algorithm refers to a set of rules/instructions that step-by-step define how a work is to be executed upon in order to get the expected results.

**Advantages of Algorithms:**

- It is easy to understand.
- Algorithm is a step-wise representation of a solution to a given problem.
- In Algorithm the problem is broken down into smaller pieces or steps hence, it is easier for the programmer to convert it into an actual program.

** Link for the Problem** –

**Counting Sort 2**– Hacker Rank Solution

Counting Sort 2 – Hacker Rank Solution

**Problem:**

Often, when a list is sorted, the elements being sorted are just keys to other values. For example, if you are sorting files by their size, the sizes need to stay connected to their respective files. You cannot just take the size numbers and output them in order, you need to output all the required file information.

The *counting sort* is used if you just need to sort a list of integers. Rather than using a comparison, you create an integer array whose index range covers the entire range of values in your array to sort. Each time a value occurs in the original array, you increment the counter at that index. At the end, run through your counting array, printing the value of each non-zero valued index that number of times.

For example, consider an array . All of the values are in the range , so create an array of zeroes, . The results of each iteration follow:

i arr[i] result 0 1 [0, 1, 0, 0] 1 1 [0, 2, 0, 0] 2 3 [0, 2, 0, 1] 3 2 [0, 2, 1, 1] 4 1 [0, 3, 1, 1]

Now we can print the sorted array: .

**Challenge**

Given an unsorted list of integers, use the counting sort method to sort the list and then print the sorted list.

*Hint:* You can use your previous code that counted the items to print out the actual values in order.

**Function Description**

Complete the *countingSort* function in the editor below. It should return the original array, sorted ascending, as an array of integers.

countingSort has the following parameter(s):

*arr*: an array of integers

**Input Format**

The first line contains an integer , the length of . The next line contains space-separated integers where .

**Constraints**

**Output Format**

Print the sorted list as a single line of space-separated integers.

**Sample Input**

100 63 25 73 1 98 73 56 84 86 57 16 83 8 25 81 56 9 53 98 67 99 12 83 89 80 91 39 86 76 85 74 39 25 90 59 10 94 32 44 3 89 30 27 79 46 96 27 32 18 21 92 69 81 40 40 34 68 78 24 87 42 69 23 41 78 22 6 90 99 89 50 30 20 1 43 3 70 95 33 46 44 9 69 48 33 60 65 16 82 67 61 32 21 79 75 75 13 87 70 33

**Sample Output**

`1 1 3 3 6 8 9 9 10 12 13 16 16 18 20 21 21 22 23 24 25 25 25 27 27 30 30 32 32 32 33 33 33 34 39 39 40 40 41 42 43 44 44 46 46 48 50 53 56 56 57 59 60 61 63 65 67 67 68 69 69 69 70 70 73 73 74 75 75 76 78 78 79 79 80 81 81 82 83 83 84 85 86 86 87 87 89 89 89 90 90 91 92 94 95 96 98 98 99 99`

**Explanation**

Once our counting array has been filled, loop from index to the end, printing each value times.

Counting Sort 2 – Hacker Rank Solution

import java.util.Scanner; /** * @author Techno-RJ * */ public class CountingSort2 { public static void main(String[] args) { Scanner sc = new Scanner(System.in); int N = sc.nextInt(); int a[] = new int[N]; int b[] = new int[100]; int c[] = new int[N + 1]; for (int i = 0; i < N; i++) { a[i] = sc.nextInt(); } for (int i = 0; i < N; i++) { b[a[i]]++; } for (int i = 1; i < 100; i++) { b[i] = b[i] + b[i - 1]; } for (int j = 0; j < N; j++) { c[b[a[j]]] = a[j]; b[a[j]] = b[a[j]] - 1; } for (int j = 1; j <= N; j++) { System.out.print(c[j] + " "); } sc.close(); } }