15821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles)/* 25821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * methods/gauss.c 35821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 45821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * Calculate the sum of a given range of integer numbers. 55821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 65821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * Somewhat of a more subtle way of calculation - and it even has a story 75821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * behind it: 85821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 95821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * Supposedly during math classes in elementary school, the teacher of 105821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * young mathematician Gauss gave the class an assignment to calculate the 115821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * sum of all natural numbers between 1 and 100, hoping that this task would 125821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * keep the kids occupied for some time. The story goes that Gauss had the 135821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * result ready after only a few minutes. What he had written on his black 145821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * board was something like this: 155821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 165821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 1 + 100 = 101 175821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 2 + 99 = 101 185821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 3 + 98 = 101 195821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * . 205821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * . 215821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 100 + 1 = 101 225821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 235821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * s = (1/2) * 100 * 101 = 5050 245821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 255821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * A more general form of this formula would be 265821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 275821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * s = (1/2) * (max + min) * (max - min + 1) 285821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 295821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * which is used in the piece of code below to implement the requested 305821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * function in constant time, i.e. without dependencies on the size of the 315821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * input parameters. 325821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) * 335821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) */ 345821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) 355821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles)#include "gauss.h" 365821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) 375821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) 385821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles)int gauss_get_sum (int min, int max) 395821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles){ 405821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) /* This algorithm doesn't work well with invalid range specifications 415821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) so we're intercepting them here. */ 425821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) if (max < min) 435821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) { 445821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) return 0; 455821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) } 465821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) 475821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles) return (int) ((max + min) * (double) (max - min + 1) / 2); 485821806d5e7f356e8fa4b058a389a808ea183019Torne (Richard Coles)} 49