UVa 10161 Ant on a Chessboard (简单数学)
2013-09-14 12:43
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10161 - Ant on a Chessboard
Time limit: 3.000 secondshttp://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=99&page=show_problem&problem=1102
Background
One day, an ant called Alice came to an M*M chessboard. She wanted to go around all the grids. So she began to walk along the chessboard according to this way: (you can assume that her speed is one grid per second)At the first second, Alice was standing at (1,1). Firstly she went up for a grid, then a grid to the right, a grid downward. After that, she went a grid to the right, then two grids upward, and then two grids to the left…in a word, the path was like a
snake.
For example, her first 25 seconds went like this:
( the numbers in the grids stands for the time when she went into the grids)
25 | 24 | 23 | 22 | 21 |
10 | 11 | 12 | 13 | 20 |
9 | 8 | 7 | 14 | 19 |
2 | 3 | 6 | 15 | 18 |
1 | 4 | 5 | 16 | 17 |
4
3
2
1
1 2 3 4 5
At the 8th second , she was at (2,3), and at 20th second, she was at (5,4).
Your task is to decide where she was at a given time.
(you can assume that M is large enough)
Input
Input file will contain several lines, and each line contains a number N(1<=N<=2*10^9), which stands for the time. The file will be ended with a line that contains a number 0.Output
For each input situation you should print a line with two numbers (x, y), the column and the row number, there must be only a space between them.Sample Input
820
25
0
Sample Output
2 35 4
1 5
题意:找到数字对应的行和列。
思路:找规律,奇数行,起始为行数的平方。偶数列,起始为列数的平方。行和列有与数字匹配的规律。依次确定所在的行和列。
完整代码:
/*0.012s*/ #include<cstdio> #include<cmath> int main(void) { int sqr, n, x, y, corner; while (scanf("%d", &n), n) { sqr = (int)sqrt(n - 1) + 1; corner = sqr * sqr - sqr + 1; if ((sqr & 1) == 0) { if (n >= corner) { x = sqr; y = sqr - (n - corner); } else { x = sqr - (corner - n); y = sqr; } } else { if (n >= corner) { x = sqr - (n - corner); y = sqr; } else { x = sqr; y = sqr - (corner - n); } } printf("%d %d\n", x, y); } return 0; }
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