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Diffstat (limited to 'C++/FindSpiralNumber.cpp')
| -rw-r--r-- | C++/FindSpiralNumber.cpp | 179 |
1 files changed, 179 insertions, 0 deletions
diff --git a/C++/FindSpiralNumber.cpp b/C++/FindSpiralNumber.cpp new file mode 100644 index 0000000..78e1681 --- /dev/null +++ b/C++/FindSpiralNumber.cpp @@ -0,0 +1,179 @@ +#include <iostream> + +using namespace std; + +int main() +{ + int x, y; + cout << "x = "; + cin >> x; + cout << "y = "; + cin >> y; + + int n, v = max(abs(x), abs(y)), g = 8 * (v * (v + 1) / 2); + + if (y == v || x == v) { // Top row or right column + n = g - x + y - 6 * v; + } + else { // Left column or bottom row + n = g + x - y - 2 * v; + } + + printf("n = %d", n); + + return 0; +} + +/* -------------- + * Task condition + * -------------- + * You have a spiral of whole numbers, starting from 0, like this: + * + * 36 < 35 < 34 < 33 < 32 < 31 < 30 + * V ^ + * 37 16 < 15 < 14 < 13 < 12 29 + * V V ^ ^ + * 38 17 4 < 3 < 2 11 28 + * V V V ^ ^ ^ + * 39 18 5 0 > 1 10 27 ... + * V V V ^ ^ ^ + * 40 19 6 > 7 > 8 > 9 26 51 + * V V ^ ^ + * 41 20 > 21 > 22 > 23 > 24 > 25 50 + * V ^ + * 42 > 43 > 44 > 45 > 46 > 47 > 48 > 49 + * + * The distance between two neighbouring numbers is 1, meaning 0 is at (0;0), 1 is at (1;0), 38 is at (-3;1). + * You are given the coordinates of a number and you have to find the actual number. + * + * -------------------------- + * Explanation of my solution + * -------------------------- + * + * My solution is a very mathematical one. First, I divide the spiral into squares, + * depending on the offset of 0;0. + * Example: + * - Square 1 (because x and y are between -1 and 1 (one of them is always 1 or -1)): + * 4 < 3 < 2 + * V ^ + * 5 1 + * V + * 6 > 7 > 8 + * + * - Square 2 (because x and y are between -2 and 2 (one of them is always 2 or -2)): + * 16 < 15 < 14 < 13 < 12 + * V ^ + * 17 11 + * V ^ + * 18 10 + * V ^ + * 19 9 + * V + * 20 > 21 > 22 > 23 > 24 + * + * - Square 3 (because x and y are between -3 and 3 (one of them is always 3 or -3)): + * 36 < 35 < 34 < 33 < 32 < 31 < 30 + * V ^ + * 37 29 + * V ^ + * 38 28 + * V ^ + * 39 27 + * V ^ + * 40 26 + * V ^ + * 41 25 + * V + * 42 > 43 > 44 > 45 > 46 > 47 > 48 + * + * And so on. I call the number of the square "v". + * We can find it by getting the absolute value of both coordinates and get the biggest number. + * + * Then there is the biggest number in the square, the one in the bottom right corner, I call that "g". + * g for square 1 (v = 1) is 8, for v = 2: g = 24, for v = 3: g = 48 and so on. + * We can see that each g is divisble by 8, but the multiplier is slightly tricky to find. + * The multiplier is the sum of all whole number from 1 up until v. + * + * Example: + * v = 2 + * g = 8 * (Sum of numbers from 1 to v) = 8 * (1 + 2) = 8 * 3 = 24 + * + * v = 3 + * g = 8 * (Sum of numbers from 1 to v) = 8 * (1 + 2 + 3) = 8 * 6 = 48 + * + * Then, we divide the whole square into two corners. We take the diagonal from top left to bottom right, and check in which part the coordinates are. + * We do that because we have two formulas. In brief, what they do is tranform the coordinates into the number from which we'll subtract from g. + * + * Example: + * v = 3, g = 48 + * + * Lets take a look at the formula for the bottom of the square. We aren't interested in g, so the important part is "x - y - 2*v". + * What it does is make the coordinates for x and y correspond to a number from -12 to 0. + * So this: + * 36 + * V + * 37 + * V + * 38 + * V + * 39 + * V + * 40 + * V + * 41 + * V + * 42 > 43 > 44 > 45 > 46 > 47 > 48 + * Becomes: + * -12 + * V + * -11 + * V + * -10 + * V + * -9 + * V + * -8 + * V + * -7 + * V + * -6 > -5 > -4 > -3 > -2 > -1 > 0 + * + * "- 2 * v" is -6, the number in the bottom left corner. Then, if we increase Y (meaning we want to go up the left column), + * we want the number to also decrease (make it further away from 0). We also have to account for X, because there it's always -3. + * So, we need them to sum up to 0 when we're on the bottom left corner, so we can just subtract Y from X. As we said, + * X is always -3 on the left column, so by increasing Y, we also increase the negative number. + * + * Ok, here are some example numbers: + * X | Y | X - Y + * ---|----|------ + * -3 | -3 | 0 + * -3 | -2 | -1 + * -3 | 0 | -3 + * + * This actually works out for us just fine when we're traversing the bottom row. There, Y is always -3, and + * when increasing X we want to increase our number (make it close to 0). So, X - Y become a positive number, + * which summed up with the negative number ("-2*v") makes the result number closer to 0, which is what we want. + * + * Here are more example numbers: + * X | Y | X - Y + * ---|----|------ + * -3 | -3 | 0 + * -2 | -3 | 1 + * 0 | -3 | 3 + * + * The formula for the top of the square (top row and right column) works the same , but there our corner number isn't "-2*v" but "-6*v", + * and we want the reverse effect: increase number (make smaller) on increasing X and decerease number on incrasing Y, + * so we make "X - Y" to be "Y - X" + * + * -13 < -14 < -15 < -16 < -17 < -18 < -19 + * ^ + * -20 + * ^ + * -21 + * ^ + * -22 + * ^ + * -23 + * ^ + * -24 + */ |