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| 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 |
| 38 int 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 } |
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