# UVa 11462

## Summary

We have ${\displaystyle n}$ numbers (from 1 to 100) that represent certain ages, now we need to sort this ages, but in the problem statement say that the size of the input it's ~25Mb, pretty big!.
This problem is solvable with O(${\displaystyle nlogn}$) sorting algorithm provided in the library (qsort from stdlib.h or sort from algorithm).
Solutions implementing O(n) counting sort algorithm (explained below) and using scanf/printf for input/output clock at 0.400 to 0.600s.
Better run time can be achieved by optimizing input and output routine with fread/fwrite.

## Explanation

Instead of normally put the ages in a vector of size ${\displaystyle n}$, and apply a sort algorithm, one can store the times that appear a number in a vector of size 101 and print the solution based in how many times appeared the numbers from 1 to 100. For the second test case, we have:

```[1] = 1
[2] = 2
[3] = 2
[4] = 0
[5] = 0
.
.
.
[100]=0
```

```5
3 4 2 1 5
5
2 3 2 3 1
0
```

## Output

```1 2 3 4 5
1 2 2 3 3

```