10161 - Ant on a Chessboard
Root ::AOAPC I: Beginning Algorithm Contests (Rujia Liu) :: Volume 1. Elementary Problem Solving :: Maths - Misc |
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10161 - Ant on a ChessboardTime limit: 3.000 seconds |
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 |
5
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
8
20
25
0
Sample Output
2 3
5 4
1 5
题解
代码示例
/**** *@PoloShen *Title:UVa 10161 */ #include <iostream> #include <cstdio> #include <cmath> using namespace std; void solve(int n){ int k = floor(sqrt(double(n))); if (k * k == n){ if (k&1) printf("%d %d\n", 1, k); else printf("%d %d\n", k, 1); } else { int t = n - k * k; int m = t % (k + 1); if (k & 1){ if (t <= k + 1) printf("%d %d\n", t, k + 1); else printf("%d %d\n", k + 1, k + 1 - m); } else { if (t <= k + 1) printf("%d %d\n", k + 1, t); else printf("%d %d\n", k + 1 - m, k + 1); } } } int main(){ int n = 0; while (cin >> n && n) solve(n); return 0; }