Counting Sort 1

Comparison Sorting

Quicksort usually has a running time of n*log(n) , but is there an algorithm that can sort even faster? In general, this is not possible. Most sorting algorithms are comparison sorts, i.e. they sort a list just by comparing the elements to one another. A comparison sort algorithm cannot beat n×log(n) (worst-case) running time, since n×log(n) represents the minimum number of comparisons needed to know where to place each element. For more details, you can see these notes (PDF).

Alternative Sorting

However, for certain types of input, it is more efficient to use a non-comparison sorting algorithm. This will make it possible to sort lists even in linear time. These challenges will cover Counting Sort, a fast way to sort lists where the elements have a small number of possible values, such as integers within a certain range. We will start with an easy task - counting.

Challenge

Given a list of integers, can you count and output the number of times each value appears?

Hint: There is no need to sort the data, you just need to count it.

Input Format

There will be two lines of input:

  • the size of the list
  • space-separated numbers that make up the list
    Output Format
    Output the number of times every number from to (inclusive) appears on the list.

Constraints

100<=n<=10^6
0<=x<100 (x is integer)

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

0 2 0 2 0 0 1 0 1 2 1 0 1 1 0 0 2 0 1 0 1 2 1 1 1 3 0 2 0 0 2 0 3 3 1 0 0 0 0 2 2 1 1 1 2 0 2 0 1 0 1 0 0 1 0 0 2 1 0 1 1 1 0 1 0 1 0 2 1 3 2 0 0 2 1 2 1 0 2 2 1 2 1 2 1 1 2 2 0 3 2 1 1 0 1 1 1 0 2 2

Explanation

The output states that 0 appears 0 times, 1 appears 2 times, 2 appears 0 times, and so on in the given input array.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

int a[100];
int main() {
    int n,val;
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>val;
        a[val]++;
    }
    for(int i=0;i<100;i++){
        cout<<a[i]<<" ";
    }
    return 0;
}