1/*
2 *  methods/gauss.c
3 *
4 *  Calculate the sum of a given range of integer numbers.
5 *
6 *  Somewhat of a more subtle way of calculation - and it even has a story
7 *  behind it:
8 *
9 *  Supposedly during math classes in elementary school, the teacher of
10 *  young mathematician Gauss gave the class an assignment to calculate the
11 *  sum of all natural numbers between 1 and 100, hoping that this task would
12 *  keep the kids occupied for some time. The story goes that Gauss had the
13 *  result ready after only a few minutes. What he had written on his black
14 *  board was something like this:
15 *
16 *    1 + 100 = 101
17 *    2 + 99  = 101
18 *    3 + 98  = 101
19 *    .
20 *    .
21 *    100 + 1 = 101
22 *
23 *    s = (1/2) * 100 * 101 = 5050
24 *
25 *  A more general form of this formula would be
26 *
27 *    s = (1/2) * (max + min) * (max - min + 1)
28 *
29 *  which is used in the piece of code below to implement the requested
30 *  function in constant time, i.e. without dependencies on the size of the
31 *  input parameters.
32 *
33 */
34
35#include "gauss.h"
36
37
38int gauss_get_sum (int min, int max)
39{
40	/* This algorithm doesn't work well with invalid range specifications
41	   so we're intercepting them here. */
42	if (max < min)
43	{
44		return 0;
45	}
46
47	return (int) ((max + min) * (double) (max - min + 1) / 2);
48}
49